Should your cooling fans be running all the time?

By fans, I assume it has more than one. One of these fans will run continuously when the A/C is on. The other fan should only run when needed to cool the engine down. In stop and go city driving in the summer with the A/C on, both fans may very well run continuously. At highway speeds, only the A/C fan should normally run. Sounds like you need to have your cooling system serviced. A complete drain and flush of the cooling system and a replacement of the thermostat may help. Also make sure the radiator external fins are clean and not clogged with bugs and debris.