Like OP I also have a t420s. It always had overheating issues. A few months after purchase, back in 2012, I even sent if for warranty repair because it routinel

Like OP I also have a t420s. It always had overheating issues. A few months after purchase, back in 2012, I even sent if for warranty repair because it routinely got "too hot to touch" and the fan kept going at insane speeds and the CPU throttling. My version only has an integrated GPU (Intel HD3000). When it came back from warranty I guess they replaced the thermal paste and installed some better Fan driver or something. The laptop still overheats on heavy loads occasionally but I have used it ever since (I can only spend on a new laptop every 10 years max). This year (2020) I completely dissembled it and replaced the thermal paste with new good quality one. It still overheats and throttles. Back then (2012) I chose this laptop mostly going on ThinkPad reputation for easy upgradeability/ repairability. Boy did I get unlucky... what a bad choice. It's the hardest laptop to disassemble I have ever had the displeasure to work on. To get to the fan assembly you literally have to remove every other component. In retrospect the reason for this is obvious. The t420s was supposed to be a slim version of the t420 (which by then was already considered thick as a tank). I guess in a away the t420s was Lenovo's first attempt at a proper slim portable laptop. Unfortunately for me the result was a slim, hard to disassemble, short battery life, overheating mess...