kahuna, the heater will take some time to get the tap water up to temp. Once it does, it will cycle with a more normal pattern. You're going to need the tank very warm if fishless-cycling by adding houshold ammonia is what you want to do (88-89degF). Make sure your ammonia has no dyes, perfumes or surfactants in it. I had a hard time finding this when I did my FLCs. Found it at the dollar store of all places. "Austins" brand ammonia. Anything other than ammonia and water in the product you're using and you'll be completely changing the water in your tank to replace it with the right stuff.
Personally, the only way I'd do an ammonia/fishless cycle again is if I had ABSOLUTELY no access to used decor and/or media. Like suggested, if you can, skip the ammonia, load your new tank with a pound or three of used gravel in a panty hose from a healthy established tank. Also add some used bio media from the established tank's filter too, then add some fish. Like any cycling method, this will require daily water parameter measurements in ppm for ammonia, nitrite, nitrate and can require more than weekly water changes.
The last 3x I've done the used decor/media thing with a "fish-in" cycle, I never saw even a fraction of a ppm of ammonia or nitrites. Nitrates slowly came up. Regardless, I still did my weekly water changes of 30-50%