This paper proposes the idea that the observed dependence of stellar activity cycles on rotation rate can be a manifestation of a stronger dependence on the effective temperature. Observational evidence is recalled and theoretical arguments are given for the presence of cyclic activity in the case of sufficiently slow rotation only. Slow rotation means proximity to the observed upper bound on the rotation period of solar-type stars. This maximum rotation period depends on temperature and shortens for hotter stars. The maximum rotation period is interpreted as the minimum rotation rate for operation of a large-scale dynamo. A combined model for differential rotation and the dynamo is applied to stars of different mass rotating with a rate slightly above the threshold rate for the dynamo. Computations show shorter dynamo cycles for hotter stars. As the hotter stars rotate faster, the computed cycles are also shorter for faster rotation. The observed smaller upper bound for rotation period of hotter stars can be explained by the larger threshold amplitude of the α-effect for onset of their dynamos: a larger α demands faster rotation. The amplitude of the (cycling) magnetic energy in the computations is proportional to the difference between the rotation period and its upper bound for the dynamo. Stars with moderately different rotation rates can differ significantly in super-criticality of their dynamos and therefore in their magnetic activity, as observed.