My Pentium 4 3.4 GHz is running hot even with a new fan on my case's heatsink (80mm rated at ~ 40 CFM). If I stress the CPU, it goes over Intel's maximum temperature rating. I'm contemplating putting in a "PCI cooler" (i.e. a fan that fits into an empty PCI slot) to see if I could get better airflow in the case. The slot isn't far from the processor and heatpipes that lead from the processor to the fan, so I'm hopeful this would help, but not entirely certain. Thoughts?
Well, sure, that would increase airflow. But you could try liquid cooling or myriad other options for additional cooling. Cheapest would be to ensure the cleanliness of the heatsink, and apply a fresh coating of performance thermal paste to the processor after wiping clean the current paste with a clean, non-static-building, cloth that leaves no fibers. Most important is cleanliness. You can remove the heatsink, and dust it separate from the rest of the components with some canned air.
Your idea should work fine, but probably won't knock your socks off with results. Look into alternative fans for the CPU itself, and make sure nothing is wrong with the current fan/heatsink/grease/CPU stack. Overheating shouldn't be occurring in the first place, so it doesn't hurt to check.