I guess rincing your gravel with warm (not hot!!!) water won't kill all bacteria, so you don't have to completely recycle your tank, especially when you don't change your filter media (I don't know what kind of filter you are using...) Water changes shouldn't affect the cycle in any way, since the bacteria are located in the substrate and filter, not in the water (I'm not 100% positive about this one, though).
I'd just set-up your tank, leave it running for two or three days, drop in some expendable fish (goldfish or guppies or whatever fish you hate :laugh: ), and see what happens. If it's all cool after a week, you could start populating your tank with normal (ie. cool) fish again.
I had a somewhat similar situation a short while ago: I have moved to a new house about a month ago, and I replaced more than half the gravel in the process. I kept about 40% of the old gravel, with the new gravel on top of that. Besides that, I kept about 25% of the 'old' water: the rest came straight from the tap ('treated' with Aquaclear). I didn't replace the filter media, and used plants, rock and wood from the old setup. None of my fish died because of all this... Fish are more hardy than many people think.