tlc5940 and led strips

A heat sink can only help a bit. There are calculations where you use a hypercritical infinite heat sink and that is still not big enough.
Have a read of this:-
http://www.thebox.myzen.co.uk/Tutorial/Power.html
And the examples page.
Yes they make clip on heatsinks for ICs if you want to spend the money but they can only help so much.