The iMac does have internal fans - not sure how many there are in yours, but it definitely has some.
The top does often get fairly hot to touch - I believe the hot air vents through the slots at the top back edge. If you haven't already, it's a good idea to vacuum all the air ventilation areas from time to time (whilst the Mac is switched off). The places to do are:
- The bottom edge where the speakers and RAM slots are.
- The circular vent on the back behind the stand.
- The vent slots along the top back edge of the computer.
Doing this can help keep the cooling of the Mac at optimum performance.
All that said, I suspect that your Mac is running at normal temperatures unless you are experiencing other issues - random shutdowns, perhaps.