You are going to have minor fluctuations in temperature unless you really have a stable environment, forutunately these are buffered by the mass of water itself. It acts like a slow responding temperature regulator. To get a feel for this just heat up a big pot of water and see how long it takes to cool to room temperature on it's own, covered. In general though, you are shooting for stability over precision. Temperature swings are usually what most people shoot to avoid, although much of this is fine (ie a few degrees is no big deal). What you don't want to have is pitching at high temps and leaving it warm as this is a sure way to produce copious amounts of esters and some nasty stuff you don't want in there, mainly higher alcohols. Pitch cool, and if the yeast brings itself up that is fine as long as it doesn't get out of hand early on. The lag phase of the yeast is a crucial time, and you want to keep it as stable as possible at that time. Now if you are trying to fine tune the flavor profile that the yeast produces then you will begin to play with temperature, but to begin pitch low and if it rises on it's own it's ok.
As for the carbonation it is a toss up. I have found a week in a warm place followed by sending it to cold storage (55 °F or so) is great for conditioning. Although, sometime I just place the cases directly into a cooler place. This in general, extends the carbonation period...but usually you are going to let the beer sit at least 3 weeks anyways and in that time they are pretty much fully carbonated. The only caveat is that if you ran a high gravity batch, your yeast might not be sufficient to carbonate to what you want so that is another thing to consider if your starting gravity is over 60.
All of these different methods may produce noticeable (yet usually very subtle) differences, you have to play to see what you like! Consider temperature as one of the biggest tools to affect flavor and it opens another dimension in the process. Again, pitch low is always a good idea.