We investigate the time dependence of the space radius and the internal space radius in a seven-dimensional Kaluza-Klein theory where both the spacelike sections and sections of internal space are 3-spheres. For an action consisting of a single, dimensionally continued, four-dimensional Euler form, the cosmological constant in spacetime vanishes. It is shown that for equations of state describing a radiation filled spacetime and an empty internal space, the classical field equations have a solution such that the internal space radius remains constant for most of the evolution of the universe. Our numerical solution suggests that the internal space radius starts evolving from zero at a non-zero, but small, value of the space radius and quickly reaches a constant value. We analytically show that such behaviour is consistent with the equations of motion.