I do this pretty much every batch. Ales are fermented (depending on yeast and desired characteristics) at anywhere between 60 and 68, and that's the temp of the actual beer via temp probe in a thermowell. I usually pitch *below* target fermentation temp as well, and let it rise until it reaches that target.
As fermentation winds down, I ramp the temp up to ~72. For dry-hopped beers, I'll leave it at 72 during the dry hop (4-10 days) before cold-crashing and kegging. For non-dry-hopped beers, I usually have a schedule that's 2 weeks from pitching to kegging, so I probably have anywhere between 2 and 5 days storage at 72 degrees.
Pros: If the yeast are having any trouble finishing, the higher temps help them get the job done.
Cons: I don't know of any -- fermentation is going so slow at this point that you're not going to get off flavors from the higher temp, and I doubt you'll even get significant ester production.