Is thermal transfer in a vacuum proportional to temperature difference?

Conductive heat transfer is indeed linear.

However black-body radiation follows the Stefan-Boltzmann Law which states that the heat emission due to black-body radiation is proportional to the 4th power of temperature. Of course if both surfaces are at the same temperature then no net heat transfer occurs. Heat transfer is proportional to the difference of the temperatures to the power of 4. This means that it's not just the difference in temperature, but amplified by the sum of their temperatures and the sum of the square of their temperatures.

$T_1^4 - T_2^4= (T_1 - T_2)(T_1 + T_2)(T_1^2 + T_2^2)$

Thus heat transfer in a vacuum is partially proportional (conductive), and partially non linear.

Convection losses are highly non-linear, but not applicable in a vacuum.