Certain models of these tubes eliminate the ballast completely. There is a compact electronic ballast circuit built in on them. Ones without this circuit use a driver instead of a ballast. The drivers use less power and run cooler than a ballast. But as mentioned in an earlier post excessive room heat is more likely body heat than lighting. But as an electrician I still recommend changing to led lighting simply because its more efficient and eliminates nasty things in your house like harmful PCB's in ballasts and mercury in bulbs.

There are 3 types of tubes. One has a ballast circuit so you bypass the ballast in the light. Another uses a driver instead of ballast. Runs cooler and on less power. The third uses the ballast but has voltage dropping circuit to make it usable.
As an electrician I personally would use one with a driver if I didn't use strips. The advantages of LEDs are less power used no PCBs from all those ballasts and no mercury from all those bulbs.
The led lighting tubes definatly produce less heat but excess heat in the layout room is more likely from people than lights.

Brian talk to Doug Hicks, he's used the cheapy LED's on his layout and the cost is low.  When I've seen his lighting it seems fine.  My layout is in a smaller room than yours, so even though I don't have the people, with little air circulation any thing except LED's seem to be too much heat over kill for the area.

Less heat and less power used

I just replaced the CFL lights behind my valance with LED 60&40 watt bulbs and so far I'm quite happy with the light and the lower heat load. The bulbs were purchased at an Ace hardware for $5.99 each. They are dimmable so I may give that a try.

 I know a lot of people use the 4' tubes but aesthetically I just can't tolerate those things.