  We considered the Inverse Compton Scattering (ICS) of charged particles onto
photons whose distribution is a Black Body Radiation (BBR) deriving the exact
energy and angular differential distribution in the general case and in its
most useful expansions. These results can be successfully applied in high
energy accelerators experiments to evaluate the ICS contribution from the
thermal photons in the cavity as well as in astrophysics where the ICS of
cosmic rays plays a relevant role in a variety of phenomena. In particular we
show how our formulae reproduce the ICS energy spectrum recently measured at
LEP, how it could be considered a key tool in explaining the Gamma Ray Bursts
(GRB) , SGRs energy spectrum. Finally we predicted the presence of a low gamma
flux, nearly detectable at hundred of TeV from SNRs SN1006 as well as, at lower
energy (tens TeV, due to gamma ray cascading in cosmic BBR), from relic
extragalactic highest cosmic rays sources born by jets in AGN,as blazars
3C279,Mrk421,Mrk 501.
