I bought this Acer TravelMate 5744 many years ago and installed Windows 7, and two years ago it suddenly stopped working. I so monitored the hardware temperature and discovered that as it turned on, its average temperature was around 60°C and every time I used to open web browsers or some programs, its temperature reached 80-90°C (and then it used to shut down). I so opened it to find issues but nothing (not even the fan), I cleaned it, retried to start it and same issues. I kept it in my desk for 2 years and decided, few days ago, to make it work again: the first times I used it, it worked really well and I also managed to install programs with a temperature around 50°C but unexpectedly it started to returning around 60°C. So I decided to format everything and install a Linux distro (Kali as I need it for work) so I could have been able to manage more aspects of CPU and hardware, easier. But at the end of the installation of an hardware detector package, it shut down telling me the laptop has reached 89°C. I've now installed a package that lets me underclock the CPU (which is 2GHz), considering that I use it only for programming things and nothing huge or that requires very strong hardwares, at which frequency should I downclock? Or if you can suggest other solutions, it would be very helpful.
It is a common hardware problem with laptops. As a matter of fact I fixed this exact issue on the same laptop model as yours not long ago.
Most commonly the thermal paste on the CPU becomes ineffective and needs to be replaced. Or another common problem is dusty fan and/or radiator. Laptop repair shops will clean it for you at a reasonable price or you can even do it yourself with basic tools and DIY knowledge, by following countless tutorials on the internet.
Under-clocking might not be very effective since the heat will still eventually build up, but if you still want to attempt it, simply changing the frequency while also looking at the temperature over a period of a few hours should be enough.