  The radiative cooling time of the X-ray-emitting plasma near the center in
many clusters of galaxies is shorter than the age of the cluster, but neither
the expected large drop in central temperature --nor the expected mass flow
towards the pressure-depleted cluster centers-- are observed. We propose a
solution to these ``cooling flow'' problems wherein energy is supplied to the
plasma by hadronic cosmic rays (CRs). The solution requires an energy
deposition more intense and more distributed than in conventional CR models,
but this alternative model is also successful in describing the origin of CRs,
as well as the properties of gamma ray bursts and of the diffuse gamma
background radiation. The X-ray energy emitted by clusters is supplied, in a
quasi-steady state, by the hadronic CRs, which act as ``warming rays''. The
temperature distribution in the intracluster space is successfully predicted
from the measured plasma-density distribution. Four other puzzling features of
clusters can also be explained in simple terms: the discrepancy between their
``virial'' and ``lensing'' masses, their large magnetic fields, the correlation
between their optical and X-ray luminosities, and the non-thermal tail of their
X-ray spectrum.
