Q: My car runs hot, past the middle of the gauge, when stopped or sitting at idle.

I have a very well kept mitsubishi eclipse 2005...looks like new radiator cap looks good,,,when after starting after warmed up,guage will be in middle... will rise when stopped will got to 3/4 then will go back down to middle and then drive more will rise to 3/4 then back down to middle...when cold over flow will be in the middle range when sitting at night after driving over flow will be above full, then later will get sucked back down to middle range. went to my mechanic to discuss we saw guage rise then he looked at fans they came on after it was past middle...also when stopped after driving top hose should be tight,,,was hot was squeeze able same as lower. hoze.and over flow to the over full line..my mechanic felt possibly thermostat or sending unit to tell the computer to turn on the fans ( as the fans do come on after its hot) my concern is worst case head gasket or water pump...radiator also looks new.....is it possible thermostat not working correctly or fan switch.....again

My car has 11345 miles.
My car has an automatic transmission.