Let us consider matter supported by radiation against gravity. The radiative flux in this case is equal to the gradient of the gravitational potential

$ F_r = \nabla \phi = g $

The radiative flux is related to the temperature through

$ F \propto \nabla{T^4} \propto \nabla T \propto \frac{d T}{d \phi} \nabla \phi \propto g $

hence the temperature depends on the acceleration as

$ T \propto g^{1/4} $