Transient heat conduction governed by non-linear boundary conditions is solved through integral transforms. Two kinds of filters are developed using as a basis either a second or a third kind boundary condition. The developed filters are applied to solve two examples in a slab: conduction with time variable Biot number, and conduction conjugated at the boundary with convection and radiation. Both filters give results with good agreement between them. The two approaches presented in this paper extend the power of the generalized integral transform technique in efficiently solving diffusion problems with non-linearity in the boundary conditions. All details derivation of the formulae, implementation and computations are presented as Mathematica notebooks in a forthcoming book, where we also consider the cylinder and sphere geometries.