A P3 733 at stock voltage with the stock heatsink can idle in windows w/ACPI-HALT-Cooling all day long without a fan, as it's roughly 8W.
Full load is a different story. You don't need a giant heatsink (and frankly I'd be careful with on, since trying to strap a modern giant sized sink onto the socket 370 lugs is likely to result in it not making good contact, or it would have to be stapped down so tightly that it was a risk of cracking the naked P3 core.
You don't need a copper or copper bottomed heatsink, the P3 does not have high enough thermal density for it to matter at 733MHz and stock or lower vcore. The heatsink limitation is the basic fin conductivity and fin surface area. You'll want a 'sink with a lot of tall widely spaced tines and/or ideally a duct attached to either the PSU intake or the case exhaust.
Do you really need this passive? You can get a no-frills all aluminum socket A heatsink wearing a 80x25mm fan for about $6. Undervolt that fan so it runs at 5V or about 400-1000 RPM and it will live long and do so silently, with minimal dust buildup since it is such a low airflow rate.
As others mentioned lowering the vcore is a good thing to try. Depends on which coppermine stepping it is, how low you'd be likely able to go. "Some" of the mid to later steppings could do 733MHz at around 1.35-1.4V, and AFAIK none of them required as much as 1.6V to run stabily at a mere 733MHz.
However, we haven't even addressed the purpose of the system. For some uses even a P3 733 would be overkill and could be downclocked to 550MHz or even lower without any real penalty. For example one of my oldest fileservers does RAID and GbE and still has a Celeron 500 in it. It's not CPU limited, never peaks above 70% utilization and even that only for fractions of a second at a time. IOW, if you can underclock it, you can undervolt even more.
P3 did have thermal shutdown integral. I suggest you set it up, fire up CPUBurn or Prime95's Torture test and touch-test the heatsink to see how hot it is. If you can leave your fingers on for a few seconds it's cool enough (obviously Prime95 shouldn't err either).