I have a 97 corolla oil is mixing with my coolant and the temp gauge is going up

No there's no coolant in the oil and yes auto transmission there is also oil on top of the motor

If you're positive it's engine oil, the only way it can get into the cooling system is through a failed head gasket!.. You sure it's not transmission fluid in radiator from a failed transmission cooler inside of it? .. Going to need some testing to confirm problem! .. As for "oil on top of motor"...No clue, unles some was spilled.