  We use numerical simulations to compute the equation of state of a suspension
of spherical, self-propelled nanoparticles. We study in detail the effect of
excluded volume interactions and confinement as a function of the system
temperature, concentration and strength of the propulsion. We find a striking
non-monotonic dependence of the pressure with the temperature, and provide
simple scaling arguments to predict and explain the occurrence of such an
anomalous behavior. We conclude the paper by explicitly showing how our results
have an important implications for the effective forces exerted by fluids of
self-propelled particles on passive, larger components.
