Yeah, the 386's were pretty much the last CPUs you could run without some sort of heatsink. 486's and Pentiums run too hot without some sort of heatsink and/or fan.
You might be able to find a northbridge heatsink or something similar to attach to your pentium. A modern northbridge with built-in GPU is far more powerful than an old pentium. You might need to look for a heatsink that attaches with an adhesive tape (many northbridge coolers do), since I doubt anyone is still making Socket-3/4/5/7 coolers.
Enough to fry its brains out. Those old pentiums didn't have thermal shutdown protection, so they would run till they fried (though of course, DOS/Windows would stop functioning long before then). It will get too hot to touch, believe me.
Unless your plan is to see if you can catch your computer on fire, don't run that pentium without a heatsink. It will fry itself to death. It will only run maybe a minute at the most before it gets too hot, so no, you can't just turn the computer on quick to try to copy files off it (if that's what you were thinking).
Oh, I see what you're saying. No, thermal paste won't be too important. Many heatsinks back then didn't even come with paste. As long as it makes good contact, the heatsink alone should suffice.
Well, I should clarify. What speed is that processor? If you're talking 266MHz or something like that, it might be good to use paste. If its an old 100MHz, then you should be fine (I ran a 166 for years with no paste).
Ok, scrape off the old paste (from both the CPU and heatsink). That old paste might soften-up after it was heated, but you don't want to burn out your CPU discovering its too old. Stick the heatsink flush to the CPU and you should be fine.
Run it for a few minutes checking the temps with your hand. The heatsink should warm up (indicating its making good contact with the CPU), but it shouldn't get too hot to touch.
When I said "flush to the CPU", I meant make sure the heatsink surface makes complete contact with the top of the CPU.
You are saying the heatsink is still attached to the CPU? Sorry, I was under the impression that there was no heatsink attached. If the heatsink is still attached, leave it there. There should still be a good seal between the heatsink and CPU if no one disturbed the thermal paste in between them.
If it's a 100MHz or less CPU it should be fine with just the heatsink on it. Always best to apply new thermal paste of course, but if it's just a slow Pentium I wouldn't worry about it. You could even run a 100MHz or lower CPU with just a big heatsink and no fan. The original Pentium goes all the way up to 200MHz, but over 100 you really should use thermal paste. If it's an MMX CPU though then yeah you need to use thermal paste.
I've got a P1 w/ win95 that I use off and on for some DOS games that I haven't moved into DOSBox yet. Mine came with a latch heat sink and paste (old Compaq Presario). I have never replaced the paste, and that sink gets warm, but no problems.