I don't need help, I just thought I'd share what I learned in case it helps anyone else.
Earlier this year I bought an M5030 very cheap due to a 7 beep failure. The motherboard had been re-flowed twice already but the owner gave up this time. I did a gentle oven re-flow myself and it ran for a few weeks of sporadic use then failed again. I went at it a bit harder the next time and then installed lm-sensors to control the cooling fan as I see fit. Previously the fan would only run when the CPU got to 60c and would turn off again at 40c, repeat. Correctly configuring fancontrol in lm-sensors got it to run reliably in the mid 40s with around 80% CPU use. I think on any machine that's well known for heat related problems this type of programme is mandatory.
After a couple of months of reliable use I got a bit reckless and started looking at faster CPUs. It came with an AMD V140 (2.3 Ghz single core) and I've fitted an N660 (3 Ghz dual core) which has, in my limited testing, transformed it. I could previously run Youtube at 480p on some videos but would often have to drop back to 360p. Now it runs 720p full screen smoothly with no unexpected buffering or choppiness. Full screen 1080p is a little juddery but maximum resolution on this machine seems to be 1366x768 so that's irrelevant. 123 movies runs very well but I'm not familiar enough with it to know it's native resolution etc. Heat management is good and it only runs 3 - 4 degrees c higher than before.
I did update the bios up to A05 which is simple in Windows but a right pain in Mint, though this is mostly due to my ignorance of Linux basics. I don't know for certain that the update was necessary for the CPU but I'm pretty sure it is for the 8GB of RAM which is my next move. I'll update this thread when that's done.