P2 Celeron vs. P3 heat output?

Anyone know what the difference (if any) is for Pentium 2 Celerons vs. Pentium 3 FC-PGA 370 processors? I’ve got a Gateway system here with a P2-400 in it which I just gutted and am hoping to put a P3-866 into it (albeit probably at a lower than hoped clock speed — it’ll probably work out to 650MHz max due to the FSB being locked at 100MHz — purely speculation, but that’s the way brand name machines like this go), ideally with the same heatsink as was used on the Celeron. The case has one fan which is intelligent (heat-switched) which does the system and the power supply, and I’ve discovered (after literally RIPPING the processor out of its socket, because the heatsink was glued to the processor and I couldn’t get to the lever with the heatsink there) that there’s no auxillary fan power socket on the motherboard — so I’ll have fun using the stock intel cooler with the Pentium 3!

Yeah, so, if anyone knows rough heat output specs for those two it’d be great if you could post! I’m getting some more thermal goop tonight, but I still need to figure out how to work the fans… I think I’m just going to end up doing a dodgy direct-to-12V molex job with a paperclip in the worst case!