Prestor’s Pyromancer text says “Battlecry: Your next Fire spell has Spell Damage +2.”
The implication in the text is that because it does not say “this turn,” then the spell damage can be banked to be used on the next fire spell, that may be cast next turn, or the turn after ,or 3 turns down, etc… in other words, the text for this card does not say that this effect is only for the turn the card is played on.
The actual effect reflects that, though. If you play Pyromancer, you get the +2 spell damage, it’s not bound to the body, so if he somehow gets destroyed right after being played, the spell damage will still apply, and the sparkling effect is shown on your hero portrait to reflect that. However, if you end your turn without playing a fire spell, the card’s effect expires, and won’t be banked for “the next Fire spell” as the text suggests, but rather, it’s confined to just the turn you play Pyromancer on.