second brew question

I have my first beer bottled. I havn't tried it yet I need to let is sit another week or 2. I followed the extract kit instructions on this one. I let it ferment in primary only 8 days untill FG stabilized and then bottled. I'll see how it turned out.
Anyway. I planned on using a more complex extract kit for my next brew and I planned on leaving in the primary for at least 2 weeks maybe more. I know alot of people on this site say at least 3 weeks in primary.
I just wanted to know how long do I need to keep the fermentor at an ideal temperature. I live in AZ so I'm going to have to keep the fermentor in a tub of water with a towel wrapped around it and a fan on it to keep temp in low 70s. That seems like alot of trouble to keep that system maintained for 2 or 3 weeks.
Can I store the fermentor in a higher temperature (75-80F) once fermentation has slowed down or do I need to maintain a low 70s temp the whole time?

When I first started using my fermentation chiller I wondered the same thing (and had the same concern). I used the next two batches (same recipe) to see if there was any noticeable difference between maintaining the temp for 2 full weeks or just during active fermentation. I didn't notice any difference in the batches between the 2 methods, so I've always maintained temperature during active fermentation. Once the FG is reached and is stable, I don't worry about the temperature anymore.

Just to give you reassurance from someone who also lives in the desert, I concur with bradsul.