Nor do they not produce heat.Most of the forward biased current does not contribute to usable emitted light. So an LED is not that efficient at producing light in absolute terms but is vastly more efficient than incandescent lamps etc.
They might not produce infrared radiation like an incandescent lamp but they certainly produce heat and hence need some form of efficient thermal management - normally in the form of a heat sink.
http://www.ledsmagazine.com/features/2/5/8