I've seen a computer for about 8 months before without an exhaust fan, and at the end of 8 months, it completely failed. PSU burnt out, as well as some parts of the motherboard.
Not a pretty sight, and fans are cheap anyway. Get 120mm fans if your case can fit those, if not, an 80mm fan will still help. Make sure you put it behind the case (just below the PSU, assuming its a standard design case), and let it blow out.
Or you can just run it as it is, and hope the computer doesn't repeat what this other computer did