The analogy between the differential equations which describe diffusion with constant diffusivity, time-dependent diffusivity, and temperature-dependent diffusivity in non-isothermal conditions is now extended to obtain solutions for two- and three-dimensional problems. The solutions for non-isothermal conditions are derived by substitution of independent variables, and correspond to a change in scale of radial distances on varying the cooling or heating rate. The dependence of the amount transferred across the interface on the rate of change in temperature is also described, and the relative effects can be predicted by selecting suitable combinations of experimental conditions. This conclusion can be extended to diffusion-controlled growth or dissolution of particles.