Corals definitely grow faster at higher temperatures. My old halide-lit SPS tank used to stay at 83-86F and it grew SPS like weeds. My current tank I kept at 78F for about a year, and about 8 months ago I guess, I turned it up to 80F and noticed faster growth. I started adding NO3 and PO4 at that time too, so it's tough to say what helped most. Everything grows faster at higher temps though - such as algae.
87-88F is where corals start dying if the corals are used to being 84 or 85F, but if the corals are used to 78F-ish, then a relatively quick rise to 86F will usually start causing demise. What the corals are used to is the biggest thing, sudden rise is never good. What I've noticed in tanks kept at high temperatures like my old tank is that being so close to the danger zone means the tank is very high energy - high fuel. It's like gasoline VS jet fuel.
Now that you posted this though, that reminded me that I want to turn my tank up to 82F and see how it does. For client tanks, I keep them at 78-79F because lower energy, "lower fuel" tanks are easier to maintain imo.
