I'm not sure I understand your second post. In the first, I thought you were asking why a base-promoted hydrolysis may require more heat than an acid catalysed one. For that, you're right - protonation of the epoxide activates the epoxide to attack by a nucleophile, with "R-OH" being the (very good) leaving group; for the base-promoted reaction, "R-O-" is a poor leaving group, so more energy is required to drive it along.
I'm going to try to help with what I think is your question - please clarify if I've misinterpreted you and I can try again!
I think you may be asking "why not heat up the acid-promoted reaction too?". Certainly, increasing the temperature of a reaction should increase the rate. However, heating a reaction will increase the rate of ALL possible reactions - including undesirable side reactions! In the case of 1,2-diols, the pinacol rearrangement is conducted by heating in the presence of acid!
Hence, experimental conditions are often a balancing act between enough energy (heat) to enable a desired reaction to take place, but not so much that side reactions become problematic.