Yes, the V3 have, IMO, an insufficient cooler.

Here is a video guide for a cheap, but effective, mod of mine: 3dfx Voodoo 3 Cooler

Voodoo3 have only passive heatsinks so they get hot. I never installed a fan on them and they still work fine - I have 2000 and 3000 model on AGP and PCI. They all work fine.

It might also be related to a bad motherboard or PSU.

PS:
Recently I found a few of my Voodoo 1 became non-working. They've been in a storage but don't really know why would they just refused to work anymore (2 out of 5 gone bad). Also have bad experience with Geforce 3 Ti200 and Geforce 4 Ti series - have around 5 of them all non-working 🙁

@philscomputerlab That looks exactly like a working solution to the problem. I'm pretty sure I have everything I need for that. Thanks for blazing the trail.

Yes, they are all hot cards. A fan is a great solution, but you could also underclock it, especially if your CPU is really slow (Pentium II 400 and below). V3 3000 models come with a somewhat beefier cooler, so running them at 143MHz will be a lot better.
You could also force v-sync, so they never produce frames in excess of your monitor's refresh rate and as such won't be pushed 100%.

Sounds like the seller is selling some bad inventory. This stuff is old and if it's not new old stock who knows what it's been through. Or where he found a stack of them.

The heat could possibly cause solder problems over the long term due to thermal expansion and contraction. Or perhaps reduce capacitor longevity. Blind guessing and supposition. I've never had a bad Voodoo3 myself. Anecdote. 😀 I doubt they get hot enough to damage the silicon though.

Well, they do get hot but not the point of failing in days, many cards get equally or more hot. I use a couple of 3dfx cards and to be honest, more voodoo1's have died or started showing artifacts inexplicably (dying of old age presumably? 😀 ) than voodoo3's 3000 or even 2000's with the smaller heatsink. Don't forget that the 3500 was a production card with the same cooling solution as the 3000, according to my reasoning this means that the 3000 wasn't that marginally cooled.

Of course these cards are old by now, so I agree that some extra cooling might cover underlying problems due to components age/use, but this shouldn't be the case for a healthy card. Bottom line? Extra cooling never hurts, but if the card really needs it to function correctly you're just postponing the inevitable.

What is the CPU? Faster processors can push a Voodoo3 further than they were meant to, and they might heat up more that they should.

Yes. They are generating head in a big way, them V3-3000/3500's.
And phil's solution is working. I have done the same, just using cotton tread through the holes and back around the heat sink on the Voodoo3. The kind of tread that you use to bind a roast together with (rated for cooking).

Another solution is to use a zallman bracket cooler. It is one of those simple ones that you mount on top of the holes that you use to secure pci/isa/agp cards with.

I suppose you could also use this and mount a 140mm or 120mm fan hooked up to a 5V connector.

my banshee has a socket 370 cooler attached with artic alumina thermal adhesive, it runs nice and cool these days

I remember in those times reading some newspaper saying that the Voodoo3 3000 would have 183/183Mhz clock while the 2000 125/125. Who knows, maybe the choice of 166 for the 3000 could have been made by the heat produced durign testing?
By the way it's cetainly one hot chip. My V3 3000 (quiet old one with early bios 1.00.00...) heat up A LOT both on the heatsink and on the back of the pcb. But we are used to considering hot what burn our fingers even if there're chips that are probably designed safely to work at that temperature. I would hope that those kind of very complex components got tested in all kind of situation evenif the problem here is that they are not probably expected to last forever as video card. Just like usign a 80's computer today.