Okay, given the information and constraints you've described, here's a breakdown of the best practice and considerations for connecting your 10/3 SO cord to the termination strip, along with safety warnings.

Understanding the Situation Stranded Wire & Set Screws

Directly clamping a set screw onto stranded wire, while sometimes appearing to work, is generally not ideal and can lead to problems over time, especially with vibration and thermal cycling (which saunas definitely have!). The strands can splay out, leading to a loose connection, arcing, and potentially a fire hazard.

24A @ 240V

This is a significant load. A poor connection here will cause problems and is a serious safety concern.

SO Cord

SO cord is flexible and has stranded conductors. This flexibility is good, but the stranded nature needs to be addressed for the termination.

Factory Wiring Example

The factory-provided wiring with its terminated ends strongly suggests that the manufacturer is aware of the potential issues with clamping directly onto bare stranded wire.

Uninspected Termination

The inability to see the set screw type and the cavity interior makes a truly optimal solution difficult, but we can still improve the situation.

Recommended Solution and Steps

Since you don't know the exact termination screw shape, and you can't access the strip to change it, you want to maximize the surface contact area and clamping force while minimizing strand splaying.Here are the best options, in order of preference:1. Use Ferrules (Highly Recommended)

What they are: Ferrules are metal sleeves that are crimped onto the end of stranded wire, creating a solid, gas-tight connection. They provide a much larger, more even contact area for the set screw. Why they're best: They prevent strand splaying, provide excellent electrical conductivity, resist corrosion, and are generally the best practice for connecting stranded wire to screw terminals. Sizing: You'll need ferrules that are sized appropriately for 10 AWG wire. The ferrule length should be short enough to fit within the terminal block without interfering with anything. Use an insulated ferrule if possible. Crimping Tool:

Crucially, you must use a proper ferrule crimping tool. These tools are designed to create a secure, gas-tight crimp. Pliers will not work reliably. Consider a ratcheting crimper for consistent results. Installation: Strip the SO cord insulation to the correct length for the ferrule. Insert the conductor fully into the ferrule, and crimp it according to the crimping tool's instructions. Slide the ferrule into the terminal block and tighten the set screw.2. Use Pin Terminals (Second Best)

What they are: Similar to ferrules, pin terminals are metal pins that you crimp onto the end of the wire. They provide a solid pin that fits into the terminal block. Why they are good: They prevent strand splaying, provide excellent electrical conductivity, and provide a solid pin that the set screw can seat against. Sizing: You'll need pin terminals that are sized appropriately for 10 AWG wire. The pin length should be short enough to fit within the terminal block without interfering with anything. Use an insulated pin terminal if possible. Crimping Tool:

Crucially, you must use a proper pin terminal crimping tool. These tools are designed to create a secure, gas-tight crimp. Pliers will not work reliably. Consider a ratcheting crimper for consistent results. Installation: Strip the SO cord insulation to the correct length for the pin terminal. Insert the conductor fully into the pin terminal, and crimp it according to the crimping tool's instructions. Slide the pin into the terminal block and tighten the set screw.3. Tinning the Wires with Solder (Use only if options 1 and 2 are absolutely unavailable)

Downsides: Creates a rigid termination that is subject to vibration failure. The solder can creep and loosen over time, especially with heat cycling. Not generally recommended for screw terminals. This can damage the screw terminal over time. How to do it (If absolutely necessary): Carefully tin the exposed strands with solder, using just enough to bond them together. Avoid creating a large solder blob. The goal is a solid, but still relatively pliable, end. Let it cool completely. Insert into the terminal and tighten. This can damage the screw terminal over time.4.

Tightly Twist and Clamp (Least Desirable, use only as a temporary measure until you can implement a better solution)

This is the least desirable option, but better than nothing if you can't implement the options above. How to do it: Very tightly twist the exposed strands of the wire together. Fold the twisted end back on itself to increase the surface area for the screw to press against. Place the folded end under the set screw, ensuring all strands are captured. Tighten the set screw firmly, but do not overtighten and strip the threads. Important: This option requires periodic inspection and re-tightening. The strands can loosen over time, especially with vibration and thermal cycling.

Important Considerations & Safety Torque

If the sauna controller documentation provides a torque specification for the terminal screws, follow it precisely. Under-tightening leads to loose connections; over-tightening can damage the terminal block. A torque screwdriver is ideal for this.

Wire Size

Confirm that the 10 AWG wire is appropriate for the 24A load at 240V, and that the terminal block is also rated for 10 AWG wire. (It should be if the factory wiring is that size).

Strain Relief

Ensure the SO cord has adequate strain relief where it enters the sauna controller enclosure. This prevents tension on the wires at the terminals. Use a cable clamp or cord grip.

Grounding

Properly connect the ground wire (green or bare) from the SO cord to the designated ground terminal in the sauna controller. This is crucial for safety.

Inspection

After making the connections, carefully inspect them. Make sure all strands of wire are fully captured under the set screws, and that the connections are tight and secure. Give the wires a gentle tug to confirm they are well connected.

Testing

After completing the wiring, and before using the sauna, test the connections with a multimeter to ensure there is no voltage drop across the terminals.

Professional Help

If you are at all uncomfortable with any of this, hire a qualified electrician. Working with electricity can be dangerous, and a mistake can have serious consequences.

Power Off

Always disconnect power to the sauna controller at the breaker before working on any wiring.

Double-check with a voltage tester to ensure the circuit is dead.* Local Codes

Ensure that your wiring complies with all applicable local electrical codes.

Why Ferrules or Pin Terminals are Worth the Investment

While they require a small investment in tools and materials, ferrules or pin terminals significantly improve the reliability and safety of your connection. They are especially important in applications with vibration, thermal cycling, and high current loads, like a sauna. The peace of mind they provide is well worth the cost.

In summary, prioritize using ferrules or pin terminals with a proper crimping tool for a safe and reliable connection. If you can't do that right away, the tightly twisted and folded wire method is a temporary fix, but requires diligence in inspecting and re-tightening. If you are uncomfortable with any of this, call a qualified electrician. They can also inspect the terminations for you. Flag for review