No, i strongly advise you use your pc with a cooling fan.
Where do you live?
Retailers like Tigerdirect sell oem heatsinks for $9-12.
You will soon have no cpu if you run without a fan.
While you can run the cpu just on the heat sink and thermal compound, it just not recommend. You will hit the the cpu max temp very easily and kill it if you run it without the fan for to long.