Thermal paste drying over time is quite normal and occasionally reapplying it is a good idea.

The P4 will be fine. IIRC that was the first CPU with (working) thermal protection. That Means, that the CPU will throttle to keep thermals from going over certain limits to make sure it wont burn out.

The "tape" on your P3 is a thermal pad and I would replace it with thermal paste, particularly considering how old it is. Thermal paste generally is much better than pads anyway and prefarable to pads, if the tolerances between cooler and device allow it (in case of CPUs pretty much always).

Tape? As in a thermal pad? Those are thick and are meant to bridge a gap between the heat source and the heatsink surface. Thermal PASTE is for when the two surfaces make contact and it fills in the microscopic pits and uneven areas of the two surfaces for a good thermal contact.

I have a 350MHz Pentium II on a Slot 1 cartridge and I felt the same way you did, so I disassembled the whole thing and replaced all the TIM I found with Arctic Silver 5. The thing runs flippin' cold now, even though I don't have a thermal sensor for the unit.
I also picked up a 600MHz Pentium III Slot 1 cartridge for that very same computer (fastest CPU the motherboard can support), but I never disassembled it. The heatsink I got was designed to mount directly onto the CPU and had its own thermal paste on it. If it ever comes to it, I can take the heatsink off and replace the TIM, but I've not had an issue with the CPU yet.

Thank you guys for the help & suggestions. Yeah ok it's a thermal pad, now I learn a little more about computers. Well it is hard & brittle and it is falling off in flakes. I checked the tolerance and the heatsink makes direct contact with the CPU, no gap. So now that I have your reassuring advice, I will be applying thermal paste on it. Great, that was pretty easy. But I must say I had a heck of a time trying to figure out how Gateway's Intel MoBo was designed to allow removal of the CPU.
I couldn't find any temperature monitor for this P3 in the bios setup utility or in the Win 98 OS. Is such a thing possible on an old computer?

That's what this CPU is also, a Pentium III 600MHz Slot 1 cartridge. But I think my MoBo supports up to 800MHz.

I highly doubt that. If it's a Slot 1, the most it will support will be a 133MHz FSB speed. Pentium III Slot 1 cartridges went as high as around 833 MHz, if I remember correctly. The first Katmai set was limited to 100FSB like mine, but the Coppermines that came later used the 133FSB speed.

FFXIhealer wrote:

I highly doubt that. If it's a Slot 1, the most it will support will be a 133MHz FSB speed. Pentium III Slot 1 cartridges went as high as around 833 MHz, if I remember correctly. The first Katmai set was limited to 100FSB like mine, but the Coppermines that came later used the 133FSB speed.

Katmai cores were available with 133MHz bus speed, and Slot 1 went up to 1133MHz with Coppermine core.