I wasn't going to reply but then I thought "screw it"
Just to be sure we're talking about the same thing, this is about White High Performance LEDs which are generally what are used in incandescent replacements.
Also fine print. LEDs do produce some heat, although not much by themselves. It is their power supplies that need the heatsinks and are responsible for most of the efficiency loss.
Every LED replacement I've seen, used and built is the exact opposite - the LED generates most of the heat. They don't produce radiant infrared heat, (as incandescent bulbs do), but the semi-conductor junction within them produces a lot of heat that needs to be dissipated via conduction.
Maximum junction thermal temperature for LEDs is normally specified at ~150°C by manufacturers, (CREE, Luxeon, etc), in their datasheets - at that temperature the LED lifespan is greatly reduced, (eg. from ~100,000 hours @ 30°C to ~10,000 @ 150°C), and luminous output is also reduced.
LEDs are usually supplied thermally bonded to an aluminium slug, this then should be mounted on a heatsink sufficient to reduce the LEDs junction thermal temperature for extended life.
The RAB floodlight you mention uses three 13W LED chips, each of which consist of ~9 LED emitters arranged in 3 columns.
Here's a LED Junction Temperature calculation for a 6 emitter 11.76W chip:Calculating LED Junction Temperature in Lighting Applications
A calculated junction temperature of 262.9°C.
Here's a calculation for the heatsink requirements of a 14.6W LED chip:How to calculate your LED heat sink
Drivers for LEDs are very efficient these days, anywhere from 80-95% - you can get them for outputs up to 20W or more that don't need heatsinks - even the 70W versions are in small metal boxes that don't require any extra heatsinking.
The RAB 39W floodlights use the whole front of the floodlight, (reflector/housing), as one big heatsink with fins to ensure the LEDs stay cool enough to achieve their 100,000 hour rating.
If you were to open it up, remove the LEDs from the housing and just hold them while you turned it on, I pretty much guarantee you won't be holding them for long.
The exact same thing can be seen in the MR-16 (12V AC/DC) and GU-10 (90-265V AC) replacements, the LEDs are mounted on the heatsink, the drivers have none.
The author of the junction temperature calculation above mentions that ~70% of the input power to the LED is converted to heat.Fact or Fiction – LEDs don’t produce heat
And FWIW, here's an article
on how to drive an LED at over 100% efficiency but at 69 picowatts of of optical output I don't think you'll be lighting up the backyard any time soon.