We present a method to compute the magnetic susceptibility of spin systems at all temperatures in one and two dimensions. It relies on an approximation of the entropy versus energy (microcanonical potential function) on the whole range of energies. The intrinsic constraints on the entropy function and a careful treatment of boundary behaviors allow to extend the standard high temperature series expansions (HTE) towards zero temperature, overcoming the divergence of truncated HTE. This method is benchmarked against two one-dimensional solvable models: the Ising model in longitudinal field and the XY model in a transverse field. With ten terms in the HTE, we find a spin susceptibility within a few % of the exact results in the whole range of temperature. The method is then applied to two two-dimensional models: the supposed-to-be gapped Heisenberg model and the $J_1$-$J_2$-$J_d$ model on the kagome lattice.
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