Cryo coolers are not very large. They are used among other things for superconducting magnets. They require a fair amount of energy because of the thermodynamic cycle requirements, they have a lot of difference between the propellant temperature and the radiator temperature.
Qcold * Th/Tc=Qhot supposing yout propellant is at 80 K (Tc) and the radiator is at 300K (23C)(Th) then the ratio is 3,75. As cooling system are fairly inefficient we can boost that to about 7, so for every Watt removed from the cold tank, wou need to reject about 7 Watts, and the power required is 7-1 Watt = 6 Watts. So supposing the gain is 1 kW you would need a 6 kW motor to drive the cooler, or about a 8 horsepower motor, and a corresponding compressor with a nitrogen or helium cooling circuit.
You might imagine something about the size of a house furnace.
Hydrogen is a lot harger because it needs to be cooled down to about 20 K and 300/20 is 15. So you would need about 15/3.75x2x8=48 kW of about 60 hp. That's getting heavier. A very small car, perhaps.
As far as the heat gain goes, it should be quite small with highly reflective surfaces and insulation. Still the sun does put out 1,3 kW per m2, so you want to keep that sun away and your tank in the shade. With careful design you might end up with a system the size of... a room air conditioner, (windowshaker, about 1/3 hp) perhaps?
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