Those barrels with set screws are from Electronics International's newer kits. They're called 'gas tight' or 'overlap' connectors and work pretty well. If you don't like to work with those items, I'd still recommend using the instructions from JPI (very similar to E.I.s older instructions).
Some of the basics: VERY IMPORTANT to check the instructions to see if you can cut temp probe wires to correct length. Some kits, usually older, tell you not to cut certain wires. Assuming that you are using a kit that allows for cutting the wires to length, route the wires into place and trim. Strip the wires as per instructions and compare each conductor to the probe wire it will be connecting to. You'll notice that the probe wires are cut in staggered lengths so match this pattern. As the wires to be terminated are very small diameter, you'll need to double over the stripped end before crimping. When you insert the doubled end into the barrel of the ring terminal you'll see that it gives you more to crimp onto than a single strand of conductor. Crimp the ring terminal securely. Use a ratchet style crimper that will not release until the crimp is complete and stay away from the crimp style that pierces the insulation.
When you connect these wires to the probe wires, use the hardware in the correct order. Slide the heat sleeve on FIRST! Use a star washer BETWEEN the two rings to help maintain a good electrical connection and to keep the rings from rotating, which will allow them to loosen up. When both connections are complete, slide the heat sleeve over them and secure with nylon lacing string. When you secure the sleeve, notice that the connections will not touch each other because they are staggered. You'll also note how handy it is to find some of the threaded ring terminals that MCS Mike showed, above.
As for electrical resistance issues, stay away from the spade terminals from some kits. If they are crimped properly, they work well initially. After a couple of seasons, the repeated heating/cooling will cause the to become intermittent. I'm not sure if I've seen a system with spade terminals that did not develop intermittents over time.
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