No, heat and temperature are closely related but having the same temperature doesn't always mean having the same amount of heat. The definition of heat is the transfer of energy from one object to another due to a difference in temperature. Whereas temperature means how fast the molecules in an object are moving. For instance, we attribute to objects that have a high temperature that they're hot, whereas those with lower temperatures are cold. So what you're asking is an object that has molecules moving at a certain rate has the same amount of the transfer of energy from one object to another due to a difference in temperature. Ok, now I'm confused but I'm still veering towards no as my answer, that is unless anyone can persuade me as to why the answer's yes.