Ab initio simulations are the favored approach to model warm dense matter as they involve relatively few approximations and assumptions. Despite their remarkable success and significant advances in computational capability during the past decade, these simulations remain very costly. We present a new model of warm dense matter based on the concepts of the average atom and the integral theory of fluids. By design, the model is spherically symmetric which results in a gain of 2-3 orders of magnitude in computing efficiency. Starting from the quantum hypernetted-chain model for liquid metals of Chihara, we have made advances to extend its applicability to warm dense matter. While such a model necessarily involves more approximations than ab initio methods, it accounts for much of the relevant physics and offers several notable advantages. The mathematical formalism of such a model is quite distinct from that of ab initio methods and presents non-trivial numerical challenges.