An excellent book on this subject is John Macvey's "How We Will Reach The Stars" (formerly titled "Journey to Alpha Centauri.") About half the book discusses the science of star travel, and the other half is a fictional account of a generational star ship journey to Alpha Centauri. In the book, the ship velocity is assumed to be 0.02C, for a trip time of about 215 years, or eight generations. Unfortunately, the book is out of print, but may be available in libraries or at used-book web sites.

Your instinct is wrong--heat is rarely a problem in space travel. With the onboard systems required for electronics, life-support, and particularly propulsion, most space vehicles are hard-pressed to get rid of excess heat. Remember, the surrounding vacuum makes you one big fat thermos bottle. If you have a power supply capable of driving a spaceship to a measurable fraction of light speed, believe me, you will have all the heat you can handle.

Recycling and zero growth are indeed difficult problems, but solvable. This is particularly true if, as you mention, there is a powerful energy source available.