Congrats on your XT-5.Glad to hear you're enjoying it. Now, I completely understand your concern about your camera getting warm after extended use especially when taking continuous autofocus (AF-C) shots. It's perfectly normal and is a natural outcome of your camera's processor and sensor working hard to get those perfect focus shots.
Your XT-5's built-in safety features will automatically shut the camera down should it detect any overheating. Based on your tests, it looks like your camera is working perfectly fine.
To prevent any possible overheating issues, I suggest adjusting some settings such as reducing the time your camera stays on standby mode or turning it off between shots. You could also avoid using the "high" heat setting for an extended duration and take some breaks between long sessions to let your camera cool down.
I'm four months in and love my X-T5, no problems at all. For me it came down to format choice, APSC. The brand choice became Sony or Fuji as Canon lens selection seems lacking. Then read up strengths and weaknesses of the two. But physically looking at the camera made the difference. I have XL hands and the Sony actually felt too small to hold. I preferred Fuji handling but the big difference was the dials. I could see how to adjust ISO, aperture, and shutter speed without instruction. Took me back to days of shooting film. I just wanted to use it. I don't like wading through menus and I don't have to with this camera. It has a ton of features I haven't used but I appreciate that I can go out and have fun, taking great stills, and learning the advanced stuff at a very slow pace. I've only shot a couple videos and have no idea what to do with the histogram. I'm not sure I care, love the camera. As for 4 vs. 5, that's hard to say. I don't want to video of myself so I prefer the tilt screen on the 5. The resolution increase isn't a bad thing, I trim my shots quite of bit and more res helps with that. I kinda wanted the latest and hopefully greatest. But if the dollar savings is enough to help out your lens budget then go for it.