i think the problem is that the 7805 can only pull 1 amp max, so anything under that, there will be a ton of voltage to dissipate as heat and if your pulling 1 amp on the 5 volt rail, then you should be using a TO-3 size regulator. I think Alex's design expects a huge draw from the regulator, and in practice, this does not really occur and as a result, the resistor does not really do much Not that hot. Thats what i have been using until now and it does not even get half as hot, and thats with 4 sids and cores with high current LEDs