Letting my fermentation temp gradually rise...

The ester profile during fermentation is mostly completed in the first three days . . . so yes, you have the gist of it.

Yeast love high temps, they would be happy in the 80s or 90s, but they would spin off undesirable flavor compounds like fusel alcohols. This is what you want to avoid. It is common to allow ferm temps to creep up in the later stages. I personally wait about 4-5 days then do a single digit increase daily for a couple of days. If doing a lager (ferm'ing in the 50s) you want to actively raise the temp to the 60s in the later stages. If doing an ale, common ferm temps in the 60s usually take care of all the diacetyl, but it doesn't hurt to bump it a little. I move temps slowly because that's the way I would like to be treated if I were a microscopic fungus.

But I wouldn't recommend going wild. My room temp is in the low 80s now which isn't ideal for extended fermentation, I keep ale temps around 68-70 as the fermentation winds down. Here's a pretty good link to the science behind all of this:
http://morebeer.com/articles/conditioning

Also, be aware that the temp in your primary will initially be higher than the surrounding air. The cold water bath you describe usually works well, but be careful at the beginning to not let temps get out of control. I suggest pitching at or slightly below desired ferm temps . . . easier to raise temp than to drop it as those little yeasties reach high gear.

 

I have done the waterbath thing many times and I do what you are suggesting. I monitor the temp of the waterbath pretty regullarly because I have previously tracked the relationship between the temps of the waterbath and the beer.

I have found that for my setup, the beer is never more than 4 degrees higher than the waterbath temp in the range that I ferment. So, if you are going to ferment at 65, then I would aim for the waterbath temp to be 61-63. After 3-4 days, I can stop adding ice bottles, but I still pay attention to the waterbath temp. In my basement, the temp usually takes a day or two to rise to the ambient temp of 67, but by that point, the most active fermentation is mostly done, so the beer temp never gets to 70.

Obviously this is driven by the ambient temp and the amount of water you are using for a waterbath. I use a large cooler (60 qt I think) and the water is half way up the side of the bucket, so maybe 3-4 gallons of water. This works better in the winter when my basement is cooler vs the summer. In the summer, I usually keep adding ice for about a week, but I get a little less neurotic about it after 4-5 days.

 

You've got it. The rise in temp is to help yeast finish up, and help them from producing as much diacetyl. Most of the flavor of the yeast is created within a few days of when you pitch. With most ales, I'll throw some frozen two liters in for 3 days and let the temp rise from there. So, if you can get down to the low 60s and come up to 68 or 69, that's be really good.

Edit: Temperatures throughout would be a great place to focus for your first AG batch. If you can nail your mash temp and nail your fermentation temperature you should make a good beer.

 

Good advice, but to be a wee bit more precise... the rise in temp will help yeast clean up the diacetyl they have made (not produce less per se).