Here are a few points I'd like to make based on my experience running Dunlop's.
There isn't a huge difference in feel or grip between DOT's and slicks. You have a little more rubber on the tire with slicks, but the extra grip that provides is small for riders at a track day pace. I'd have to search for some evidence to back this up, but I bet the lap time difference from a top rider on a 600 would be pretty small. IMO tire compound will make a much bigger difference.
Slicks last longer than DOT's.
There is never any problem flipping slicks both front and rear.
Worrying too much about heat in the tires is over thinking it. In all but the coolest of conditions both slicks and DOT's are going to have more grip at any pace than than street tires. In other words if you are riding around on the track on a sunny day and the temperature is over 60 you will have more grip with race tires than you will with street tires, regardless of whether you are riding your fast pace, or ten seconds off of your fast pace. We aren't riding on Moto GP tires where just a small difference in temperature can mean a big difference in grip. If you slow down by ten seconds for a lap you are not going to crash because your tires cooled down. If you pay attention to what I say below about developing feel you'll understand what your level of grip is under almost all conditions.
Warmers are not required for race tires, but they are a good idea. The main reasons are that if you have to spend several laps getting them up to temp then you are wasting your track time. Also, depending on the track and temperature you could have tearing if you are on cold tires. For the most part heat cycles are not something you need to worry about at a track day.
I've never seen any need to run anything but medium on the front. It'll last so long that you'll be changing it out just because in your head you think you shouldn't be able to get ten days out of a front tire.
I have a little bit of a disagreement with Brad in that I think you should pick a tire, or at least a brand of tires, and stick with them so that you can learn them. We talk about grip, but there is also a "feel" that you need to come to understand. Feel is very subtle, and when you learn how to feel what a tire is telling you you'll know when you are approaching the limit of what you can get out of the tire. Notice I didn't say the tires limit, but but your own limit using that tire. Understanding what you are feeling is made more difficult if you are always running different tires.
One reason for switching to race tires besides the going faster part, is the margin of safety part. With more grip you have a bigger safety margin. A mistake that you can't recover from on street tires might be something that you can recover from on race tires. It's really very simple that the chance of suddenly losing all of that grip you have is less on a tire that has more grip.
I'm not sure if any of this helps or just muddies the water, but I think the absolute bottom line is that race tires are made for what we are doing on the track. They aren't necessary to ride at track days, but most of the time they are the best choice. If you can afford them use them.