Ultracold atomic Fermi gases can be tuned to interact strongly, where they display spectroscopic signatures above the superfluid transition reminiscent of the pseudogap in cuprates. However, the extent of the analogy can be questioned, since thermodynamic quantities in the low temperature spin-imbalanced normal state can be described successfully using Fermi liquid theory. Here we present spin susceptibility measurements across the interaction strength-temperature phase diagram using a novel radiofrequency technique with ultracold $^6\textrm{Li}$ gases. For all significant interaction strengths and at all temperatures we find the spin susceptibility is reduced compared with the equivalent value for a non-interacting Fermi gas, with the low temperature results consistent with previous studies. However, our measurements extend to higher temperatures, where we find that the reduction persists consistently with a mean-field scenario. At unitarity, we can use the local density approximation to extract the spin susceptibility for the uniform gas, which is well described by mean-field models at temperatures from the superfluid transition to the Fermi temperature.