The time evolution of the particle number density and spectrum of massive scalar particles, coupled conformally to a classical Friedman-Robertson-Walker gravitational field is followed numerically. Not only for a pure radiation cosmos, but also for one with an inflationary interlude, the density of particles produced remains constant in time. This results in a constant equivalent “temperature” scale up to the Compton time of the massive particles, and opens the possibility that during a sufficiently long inflation the energy density of the particles produced can exceed that of the radiation background.