The first time for me was with their T43. This model was mostly a platform refresh of the T42. There's a chip called a southbridge that's located below the palmrest. Between the models this chip went from 400mhz to 533mhz. Lenovo decided it wasn't important to improve the cooling, no heatsink whatsoever included on the southbridge. However, they kept ample temp sensors in the case so the fans would pulse nonstop as it failed to cool this one chip.
I had two nicknames for that laptop. The 'nut roaster' and the 'vacuum cleaner'. I eventually fixed the problem by hammering out an old copper penny and sticking with thermal compound to bridge the gap between the heatsink and chip. It wasn't perfect but it dropped the temps like 10C. The rest could be controlled with an installed fan daemon.
Personally I believe the major source of heat of the X220 comes from the Sandy Bridge processor. The next-gen Ivy Bridge in X230 has almost no performance gain, but reduces heat dissipation significantly (ironically, Ivy Bridge is also the turning point when Intel started to use crappy thermal paste in the desktop CPU packaging, leading to thermal issues...).
I own both machines and the difference is great. Also, two of my X220s from different sources all suffer with random shutdown issues, I suspect the source is the cold solder joints under the power MOSFET or a defective one (saw a troubleshoot post of a similar issue in a fourm), but it's BGA, so...
Anyway, that's why I recommend everyone who wants a X220 to get a X230. You can even replace the motherboard and the bottom case to "upgrade" the X220 to X230.
> the heatsink from the x230 can be fitted to a x220.
I believe it's virtually identical. I never heard about the X230 heatsink performs better, perhaps it's the case, I may give it a try someday...