Lighthouse,
Thermal transfer is good but more important is the electrical contact - without that its not going to get hot at all
swtxtitan,
I laughed reading that, this isn't anything quality at all.
Say it with me, 'the emitter fell off the 10mm circular engine'
Your 'small board' is the ceramic substrate the emitter is built on, so no those don't come off.
When the unit was made the emitter was supposed to be reflowed onto that circular light engine and sounds like the job was botched. It needs to be soldered back on for a few reasons, mainly electrical contact, but also thermal transfer from the center slug to the engine (and thus to the light body).
To fix this, the electrical leads need to come off.
the engine needs to be removed from the pill (the light body)
clean the back of the board (need to remove some thermal paste if you're lucky)
-a little sanding of contact pads to remove old solder
-clean contact pads w isopropal alcohol (both board and emitter)
-apply some solder paste (very little, see reflow soldering)
-reflow emitter back onto the board (takes ~30seconds start to finish)
Reassemble:
thermal paste on back of board to light pill (light body)
reconnect electrical leads
This is not the simplest diy to fix, but may be the 3rd or 4th simplest task? But if you're new it's right impossible.