Asteroid ships have the exact opposite issue from what you're thinking...30 to 65% of the volume is a metal or silicate matrix that is a heat reservoir - you'l have a harder time cooling it to local ambient than a normal ship, because that rock and metal has already been raised to shirtsleeve temps.
Umm, no it was stated to have been cooled already.
Some basic physics facts about blackbody radiation:
The magnitude of the black body radiation an object puts out is a function of both the temprature and the surface area at that temperature. At any given temprature there is a coresponding maximum frequency that is emitted, but all of the lower frequencies are also emitted, and the intensity of every such frequency increases as the temperature increases.
So the shape of a blackbody radiation sprectra is one of a increasing amplitude over frequency and it appears to be increasing at some positive power as temperature increases.
One can calculate the total energy a 273 degree K 100 ton sphere hull will radiate to within a very fine tolerance, and the exact sprectra of this is known, and is independant of what the material is.
(The power plant is OFF so no super hot radiators need be concidered, nore the proported 250 MW output from the self same power plant)
Now let us discuss how that can be spoofed:
Inflate an envelope around the hull that has the surface area of a 10,000 ton spherical hull, this envelope is opaque to light and will absorb the ship's radiated energy and re-radiate the same energy however it will do so at a lower temperature spectrum. Change the size of the envelope as needed to adjust for the temperature spectrum you desire to emit. (*use a white globe screen to create the same effect at less mass/ difficulty.)
You can have optical emitters in your hull emit 10 X the energy at a lower temperature spectrum, trying to mask the higher temperature spectrum.
Which rule set you use strongly effects your assumptions:
Book 2 1 EP = 250 MW and you can do nothing to reduce this output level or fuel use so a ship is assummed to be generating either 250 MW per EP or none. 200 ton J1 1 G ship will be producing 500 MW of power even when not maneuvering or jumping.
T4 FF&S 200 ton Jump 1 needs something like 56.8 MW (memory may be off by a MW or two, please forgive the estimate) and life support may need less than 1 MW, computers sip power at the lower levels, and you do not have to install power consuming items like G-comp or environmental gravity, and the power plant can be throttled down to the output = to the minimum size for your TL (TL 15 that's .6 MW BTW) 1G of acceleration for a merchant ship generally takes that same 56 MW that the jump drive takes, but a lot of that heat is departing the ship as fast mass in your HEPLAR exhaust. and pumping for jump has all that jump fuel as coolant for the PP, thus supplementing the normal radiators.
All the above means is that in T4 you can have a 200 ton J-1 1G ship that operates with a 60 MW power plant, that is running at about 1 MW if not pumping for jump or maneuvering, a difference of about 2 1/2 orders of magnitude compared with the BOOK 2 assumptions. Most of you know that I'm a T4 ship design gearhead. I do not see that the heat dissapation is all that great of an issue mostly due to my seeing the issue as 2 1/2 orders of magnitude smaller than the Book 2 fans see it.