  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.
