The heat sink cools your whole ship down but the effect doesn't last long. It might help reduce the damage caused by heat overspill (which will become more of an issue in 1.2) but it won't stop the lasers shutting down due to thermal overload as far as I know. A better power distributor will help, I use an A3, but I still need to keep 4 pips in weapons most of the time with a pair of beam lasers. Firing in short bursts, 1-2 seconds, is also a good idea.
The main thing I use my heat sinks for is keeping cool during a silent run into a station when I'm carrying dodgy cargo!