There are two ways this could be played.
The Resource, A Fiery Temper, (giving a troublemaker +2 power) could be played on Parasprite Swarm to quicken it up to +8 power to trigger its ability to frighten all your opponent's Friends at its Problem.
Or, A Fiery Temper could be played to skip past its +8 trigger and continue climbing in power. (Potentially going up and up and up). However, this would only force your opponent to give up on its Problem and move their characters away. (As could the first option).
If played in conjunction with a Problem that essentially traps Friends there, this could be brutal, essentially trapping opponent's Friends there to be all frightened (or facing a troublemaker that's - eventually - impossible to defeat).
Who is Gabby Gums? is a good example of this kind of Problem.
Good decks for this troublemaker would include Rarity and Princess Celestia (who, out of the regular pre-built decks could defeat this Problem).
Another good card to use in conjunction with Paraspirte Swarm might be Rainbow Dash, Goosebump Giver,
adding insult to injury with yet another opponent's Friend frightened.