My 1999 Intrepid tends to get hot after I turn my ignition off and start it again. Any suggestions?

I have an hour commute to work. While I drive to work the temp indicator is half-way or less. It is when I stop to get gas or the like. I turn the ignition off, do what I need to do, turn the ignition back on and start to go, the temp guage is 2 marks above where it needs to be and headed toward the red. When I get to work I shut it off and let it cool down. When I go out to go back home, everything is hunky dory again. Any suggestions before I ruin the engine? The fan is working.