To focus and direct it, you would have to interact with it with real physical things, which gets you right back to square one - now you have this hot thing and you don't want it hot.

Well yeah, but let's say you radiate out as planned, but near the front of the spacecraft you expand a very large reflective dish, like a lightsail, say a km across. Now you're slightly biasing the direction the heat is radiating and the spacecraft will have to move in the opposite direction. Small changes in angle of the dish will move the vector of the reflected radiant heat.

In other words, you could use the main engines to get to Alpha Centauri, then use the radiant heat for the precision maneuvers around the system.

Because of the rules of thermodynamics, in particular entropy, heat rather quickly assumes a form that can't be harnessed to any useful purpose.

Can you provide an example? I know of a nearby stellar body that gets into the double digit millions of degrees that we harness all the time.

Certainly -- our sun will eventually radiate away all its useful energy and that energy, although not lost, will assume a form that can no longer be exploited. This shows the truth of the expression "entropy increases over time". Reference:

http://en.wikipedia.org/wiki/Entropy_(arrow_of_time)