Reducing heat dissipation in linear current source used for driving a LED
Assuming I am looking at the right circuit, which you should have reposted here so people do not have to go back and forward.... 

Also assuming you wanted 0.25A per LED and they can handle that.

Your choice for Q2 is way undersized at 350mW you need at least a 1W part if not a 2W and a heat-sink would not hurt. The 2N7002P is also a MOSFET. I do not see any MOSFET circuits in your link. So this whole answer may be bogus. A MOSFET may cause this circuit to oscillate, and is not buying you anything.

R2 also needs to be at least a quarter Watt, which will be at 20C above ambient, a half Watt would be cooler. 

The LEDs themselves, at half a watt each, are your worst offenders and also need special treatment to get rid of heat.

As for reducing heat. 

With a linear solution at that range of voltages in, you don't get a choice, you need to dissipate @3W, which is not that bad for a two inch square. You can better manage the heat, but the wattage is what it is. A switching driver would be better for this high a current, and the inductors are not as expensive as you might think, not compared to a ton of heat-sink stuff. There is nothing you can do reduce the LED heat generation though, other than run them dimmer.

Anyhow, fix Q2 first to a larger NPN part that wont get so hot temperature wise.