During electrolysis water molecules are split into their constituent atoms, Oxygen gas is produced at one electrode and Hydrogen gas is produced at the other.
Electrical current is used to spilt water molecules into their constituent gases. Hydrogen is produced at one electrode and oxygen is produced at the other.
The molecules in warm water are moving quicker, meaning that the hydrogen bonds between the molecules are breaking very quickly whereas the molecules in cold water are moving much slower.
If they were the same temperature then neither, they would both be the same warmth. the difference would be the energy they give off, the cup would have a lot less energy and would cool faster in a...