No heat. Well, you must be decades ahead of the rest of the industry.
The only LEDs that don't produce 'any' (actually very little) heat are those that don't produce 'any' (actually very little) light. Even if your white LED had an efficacy of 100 lm/W (far greater than the efficacy of any white LED available today) it would have an electrical efficiency of only about 30%, so for every watt of light produced, you would still have to dispose of more than 2 watts of heat.
Check out the high brightness Luxeon LEDs at
http://www.luxeon.com. These are great LEDs with high efficiency and high brightness. However, they all have a heat sink. If LEDs don't produce any heat, why do these have heat sinks?
Vic Roberts