Heat powered engine cooling paradox

I can't get my head round this.

I'm pretty sure that you've heard of a "Stirling Engine" (If you don't, Its basically a small engine that runs on heat, you put it on top of something and it runs).

These engines have an output shaft (i.e you can attach something to them and make it spin, e.g gears).

Now what if one attached a fan to it, Which one would win? Fan or engine? They would be fighting each other, The engine would be running from the heat but its own fan would be cooling it down.

I can only think that the fan would keep it below a certain temp and as such would stop it from going above a certain RPM.

What do you think would happen?