Should. I would give it a little acclimation--put it in a tub of the 80F water, let it cool to 72, and swap away. I've never had any problems when moving media from one temp to another, so this is just being cautious
Agree w/OG. The good guy bugs are quite hardy. A greater shock would be a major pH (really KH/TDS) difference in the two systems - but slow or drip aclimatization should avoid that as well. If the water parameters other than temp are similar, it should not be a problem.