Will a new coolant radiator cap

I would start with inspecting engine for signs of a leak. Specially around the water pump. If leak found there then I would replace the water pump. If no leaks found and you have never poured anything like stop leak in your radiator (please don't use that stuff it just hides the problems and creates bigger ones in the long run) then I would start with testing your thermostat. If found to be faulty then replace it. Last but not least. You stated that it heats up on long trips on the highway then cools down quickly as you slow down. This is one sign of a possible head gasket issue.

Oh and yes a faulty cap can cause an over heating issue.

sounds like thermostat sticking would do that first cheapest option if no leaks from pump get new o ring for thermostat housing mine was leaking at housing after I replaced thermostat will save you from doing it twice.