Update: I now have the external cooler (fan tray), and have tried it out. In an ambient temperature of about 25°C, and while compiling a kernel, CPU core temperature was steady at about 55°C. So, under heavy load, the machine runs about 30° over ambient. I think the highest temperature in which I will need to work will be about 30°, so the machine should not get much hotter than 60°. I think this will be OK. I am guessing it be around 50° most of the time, going up to 60 occasionally. It should survive this, I believe. Would anyone like to comment?
(The kernel I compiled was the latest stable version. I booted the system with it, but fan cooling was still broken, unfortunately)