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positive to a negative
Both. One side of the equatioo loses energy and the other side gains it.
If you connect the positive and the negative end of a battery directly with a cable, (1) you'll get dangerously high currents, and (2) the battery will quickly run out of energy. The battery itself might also get damaged, due to the high currents.
Unless they are kept apart, they will annihilate each other with a release of energy.
temperatures differ from thermal energy because differ because thermal energy is the total energy of all particles in an object and temperature is a measure of the average energy of random motion of particles of matter.