You'd be surprised how little heat they generate- but they should be at least on one of those aluminum "star" heatsinks, running the raw LED "bead" without a heatsink for more than a few seconds will in fact cook the little beast. On the plus side, one watt white LED's are less than a quarter each ordered from China.
I have had good luck using aluminum angle bracket and channel from the local Home Depot for heat sinking, and a tube of white lithium grease for compound.
I have a homebrew LED photo strobe with over 140 watts of LED's on it now- I use a "repurposed" aluminum cable modem casing (about two pounds of thick aluminum) as the heat sink of the gods on that one.
On the subject of Power Supply- simple. ATX computer power supply, ground the "power good" line and you have a high-capacity 12v and 5v supply... fan cooled, and cheap.. free, if you cannibalize an old PC... Use a fuse though, PC power supplies can kick out quite a bit of current!