Engine Overheating

I noticed today that my engine was running at a considerably hotter temperature than it normally does... I had left it running with my daughter in it while I was checking the sign on a store to see what their hours were... When I got back in, the A/C was blowing warm air with seemed somewhat strange since it had been working a couple of minutes ago... I looked at the temperature gauge and it was right at the edge of the high red zone... I remembered someone mentioning in a recent post something about engine temperature as it relates to the speed you are travelling, so I decided to try driving it to see if it would cool off any... Once I started driving it did cool off, so I figured that there must be something wrong with the fan... I paid close attention to the temperature gauge and it went back down to normal in a couple of minutes... I completed the errands that I needed to run and once home, I looked at it a little closer... It turns out that the electric fan wasn't running... A couple of jiggles of the relay and it started back up... Apparently some oxidation in the connection... Once the electric fan was back running, the engine went back down to a normal temperature fairly quickly... So, I have to assume that the electric fan controls the air flowing through the radiator... What does the mechanical fan do?