Will the mana that has been added to your mana pool by Koth of the Hammer's -2 ability empty as your turn ends, or is the mana from the -2 ability added for the rest of the game?
Mana empties from every player's mana pool at the end of each step and phase.
500.4. When a step or phase ends, any unused mana left in a player’s mana pool empties. This turn-based action doesn’t use the stack.