I have a second-hand Thinkpad T480s that I love, I bought it for 250$ on ebay and replaced its battery because it was fried (+40$). I use it for school and it works flawlessly, around 8h of battery life in a well-configured OpenSUSE Tumbleweed. According to the specs sheet it shouldn’t be, but for some reason it is noticeably lighter than a friend of mine’s MacBook Air 2021.
What I really love about it is the ThinkDock Ultra (iirc 30$ on ebay), which lets me place the laptop on my table, and by just sliding a piece of plastic, it connects all of my peripherals in a second. I love this laptop so much that I’ll use it until it dies so hard that it can’t be fixed at all.
What you need to do is clean the dust off of your fans and ventilation filters (check guides or figure it as you go, but make sure to disconnect the battery and the fans from the mobo as soon as you open it). Then, repaste it with good thermal paste or some liquid metal if you’re feeling confident. I have liquid metal (thermal grizzly condoctonaut) on both of my laptops, and one of them which had overheated since day one, doesn’t anymore.
Oh, true, you don’t get previews of the windows inside. However, that shouldn’t be very hard to implement, so you might have luck if you ask for it to be in Plasma 6.
I prefer the T480 series (imo Thinkpad went downhill from there onwards). The non-s is a great off-road laptop, but for what OP is asking, the T480s seems like a more sensible choice.