Very well explained. Thanks for that!Updated my comment after posting, sorry. They'd do very well to begin with (assuming they were acclimatised to the seasons being reversed) because their new prey would be completely unadapted to deal with land-based predators (the natural predators of penguins are seals who attack from the water). (think humans and the dodos)
More young polar bears making it to adulthood would cause a population explosion, until the penguins ran out, then they'd be screwed.