This video with narrated commentary will help you easily get all four achievements in the Thermal level! Simply hit play and listen! If at any point you need a visual, you can check the video. Enjoy the video and happy hunting
If you're looking to get this achievement specifically, the setup (gathering the wires) starts at 7:50 and the achievement attempt (plugging in the wires) is at 11:17.
planchetflaw had some helpful tips from the comments:
If you're really struggling after numerous attempts, a good trick is to hold two wires at the same time, one in each hand. Make sure they are two that line up with two of the bottom plugs. That way, when you start, you get two plugs in for the time cost of one. Might make the difference if you are still struggling with the controls of the game.
Aside from that, I found doing all the bottom row first easier as nothing was blocking the way. Keep the upper plug ends farther back from the console so you don't try and pick up ones already connected.
You don't need to do a colour first, then another colours, etc. So plug the ends in based on whatever is closest on your set up. You can do a green end, then a red end, then a blue end, then the second green end, etc.