After 11 years of use of my PS3 (sure the past 6 were very light use) my console finally surrendered to YLOD. It is on the assistance and estimate 40USD to repair, let`s pray for it safe recovery.
Mine is a phat version with 160Gb memory uncharted bundle so I guess second or third gen.
If you do end up getting it fixed, and if you don't plan on playing online with the system, I would recommend installing custom firmware on it. About 2 years ago I bought a CECHA01 (Launch 60GB model, "fully" backwards compatible with PS2 titles). Upon getting it I tore it down to replace the thermal paste, then installed custom firmware. Once you do that, from the XMB you can hold Start+Select and it will give you a notification with the current RSX and Cell temps.
Also, by default, the fan curve on the custom firmware is much more aggressive. You can set targets for the system to keep each chip at. By default, the PS3 will let the processors go up to crazy high temperatures to keep the system quiet before it starts to ramp up the fans. I have my system set to keep both chips at 65c or below. It is much louder now than it was on stock firmware, but it'll give you piece of mind that the system won't overheat.