What I was suggesting is a reactor that turn MS into "Hot MS" that you can use in a Thermal Boiler to generate energy, then you can reinsert it back into the reactor. But that is also what you suggested, for the EXTERNAL COOLING SYSTEM. The difference with what I suggested, is that I mentionned only the GUI, and the way you would exchange heat between the reactor and the external cooling system (aka to heat the MS you will use in the Thermal Boiler) would be the equivalent of the "Coolant cells" (something that can store heat but that can also transmit it).
So Mk I would be like this:
(assuming
= Any kind of radioactive fuel,
= these coolant/exchanger cells,
= fuel you wanna breed
= why not a higher capacity coolant cell, that will hardly exchange heat but may be useful for reactors you wanna switch on/off often, aka MkIII or more)

(also assuming 3*3 grid)
MkII:
(off half of the time. The
should have a HUGE thermal capacity since IRL the annoying point with MSR is that they would theoretically cost Pu to "ignite", even though they can run "forever" with Thorium that you can replace meanwhile)
Mk III

or
(By the way, I assume you make no difference between heatS, so all the heat emited by cells goes directly into the "reactor hull", which means that every single component is at the same temperature)
MkIV/V:
:Intergrated Plating:
(Heat extremly fast, and then you have EU at a slow rate, to cool the :Intergrated Plating: down).
Breeders would be like:
:Intergrated Heat Dispenser: :Intergrated Heat Dispenser: :Intergrated Heat Dispenser:
:Uranium Ingot: :Tin Ingot: :Uranium Ingot:
:Intergrated Heat Dispenser: :Intergrated Heat Dispenser: :Intergrated Heat Dispenser:
:Intergrated Heat Dispenser: :Tin Ingot: :Intergrated Heat Dispenser:
:Tin Ingot: :Uranium Ingot: :Tin Ingot:
:Intergrated Heat Dispenser: :Tin Ingot: :Intergrated Heat Dispenser:
or MkII or more breeders:
:Uranium Ingot: :Uranium Ingot: :Tin Ingot:
:Uranium Ingot: :Uranium Ingot: :Tin Ingot:
:Tin Ingot: :Tin Ingot: :Intergrated Plating:
There would be several tiers for each components.
Once "empty" (without fuel anymore), cells could be centrifuged/electrolyzed to get depleted fuels/fuel with lower tier (Pu-->U-->Th)/some non-radioactive product if you assume the reactor is extremly efficient 
As for efficiency: Heat emitted depends on adjacent cells (and their own efficiency! so the reactor have to calculate the efficiency each tick depending on the efficiency of all cell during the previous tick! Which means you could reach extremly high efficiency if you achieve making an ever growing efficiency, but beware not to reach the limit of efficiency which is Nuclear Chain Reaction = Bomb! Btw, the reactor would explode if you reach that max efficiency, and simply overheat then melt of you don't cool it enough)
For breeding, the thing SHOULDN'T depends on global heat, but only on efficiency of adj. cells. (For realism and to get rid off design that stores tons of heat to make breeding more efficient ^^)
I hope this help a bit.