Is heat just a change in temperature?
[...] is there potential heat energy in the temperature of an object?


The energy associated with temperature is called thermal energy. If you know the heat capacity of an object, you can figure out how much energy is required to change the temperature by a certain amount.


  If heat is just a change in temperature, but temperature isn't energy, doesn't that imply that energy is created when two objects of different temperature interact [...]?


Heat is energy transferred from one object to another. When heat is transferred from a hotter to a colder object, the hotter object loses thermal energy and the colder object gains it. No energy is created.


  Where is the energy from heat and other chemical processes coming from, exactly?


A chemical reaction can give off heat because electrons can be in higher states (weak bonds) and in lower states (strong bonds). Potential energy can turn into thermal energy, and vice versa. It takes energy to melt ice, so melting ice cools down the surroundings. An explosive reaction releases energy, so it increases the temperature of the surroundings by transferring heat to it.