  We study a bilayer consisting of an ordinary superconductor and a magnet with
a spiral magnetic structure of the {\rm Ho} type. We use a self consistent
solution of the Bogolioubov-de Gennes equations to evaluate the pair amplitude,
the transition temperature, and the thermodynamic functions, namely, the free
energy and entropy. We find that for a range of thicknesses of the magnetic
layer the superconductivity is reentrant with {\it temperature} $T$: as one
lowers $T$ the system turns superconducting, and when $T$ is further lowered it
turns normal again. This behavior is reflected in the condensation free energy
and the pair potential, which vanish both above the upper transition and below
the lower one. The transition is strictly reentrant: the low and high
temperature phases are the same. The entropy further reveals a range of
temperatures where the superconducting state is {\it less ordered} than the
normal one.
