  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 $\alpha$-effect for onset of their dynamos: a larger $\alpha$ 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.
