a crapy fan is better then no fan at all... Any air movement helps. Do you atleast have a case fan? Cuz if you take the CPU fan off and there is no air movement inside the case from a case fan then its not really getting any cooling at all even with a heatsink and its gona fry.
Like someone else said, get a new better heatsink/fan for the CPU if the stock is so crappy, thats kinda the reason they make better ones.
And whats so crappy about the fan? Is it real noisy or somethin? Cuz if it isnt noisy and its just a slow, low CFM fan then removing it is only going to make the situation even worse.
On my dell the the processor only has a heatsink and no fan. But the rear case fan has ducting on it that comes out and covers the heatsink so that all the air sucked thru the case has to go over the heatsink to exit the case.