You lose all the use of the second fan essentially; I know when I bought an Enermax dual-fan, I read specifically on their site a warning about making sure that your case would accept it properly.
If you can, take it back and get a single-fan PSU (there are plenty of good single-fan PSU's, a second fan doesn't automatically make it better). If not, open the casing and disconnect the power connector for the internal fan so you're not wasting power and making more noise (even if it is a very little bit of noise). I'm of course not responsible if you electrocute yourself; don't do it if you can't do it right. I would expect that having a fan shoved very close to the top of the case will just create turbulence and noise, but if there's a little bit of space, it may help with cooling. I never really noticed any temperature differences with or without a second fan blowing in the PSU, and the air coming out of my TruPower 330W is barely even above room temperature.
Of course, you could just mod the case and put a suck-hole above the PSU fan, a little duct inside to give it a good suction.