When I start car my fan comes on but goes off right a way and car gets hot in stop and go traffic but cools down on a fast speed up what could be wrong

We've even done the water pump,heater core I just can't figure out what to do I've put 6,000 in to this stupid heat problem pluse some other work can sell it for even close to what I've done its almost bran new now can someone please help me out here any ideas?

I've tried twice but got on reply... Adios.