You are supposed to heat it, but I don't bother.
Let's say your tank is 25 degrees, and you do a 20% water change with water at only 15 degrees, in other words 10 degrees lower. That's only going to drop your average temp by 2 degrees. My chiller will do that and seems to have no negative effect. Heating up water can be a lot of jerking around, and IMO, each job should be as easy as possible, that way you are more likely to actually do it.
Also, my corals seem to like it when I dump in a heap of water at a different temperature, a few minutes later they expand right up, they think it is a new current coming in from somewhere.
And about the possible bugs in the water, the general consensus seems to be that provided you collect water from a good clean source, you are unlikely to infect your tank with any nasties.