  Although the ultraluminous infrared radio galaxy 4C12.50 at z=0.12 is a
promising candidate to reveal how radio induced feedback may regulate star
formation in galaxies, we find no solid evidence for current or past impact of
this mechanism on the evolution of this system, neither by clearing out the
dusty central cocoon efficiently, nor by suppressing star formation. We study
in detail for the first time the hot (>~1500 K) molecular gas in this object.
The potential impact of the radio jet on this gas phase, as well as on the star
formation activity, are investigated. 4C12.50 hosts (2.1+/-0.4)x1e4 Msun of hot
molecular gas. An unusually high rotational temperature T =3020+/-160 K is
inferred. The molecular gas mass obeys a power law temperature distribution
d(M(H2))/dT ~ T^-5 from T~300 K and up to ~3000 K. Both results support that
shocks (probably induced by the radio jet) contribute to the heating and
excitation of the hot molecular gas. A molecular outflow is not detected. The
coupling of the outflowing ionized and neutral outflows with the hot molecular
gas is poor. We find no evidence for star formation supression. NIR and MIR
integral field spectroscopy at very high spatial resolution (for instance, with
the JWST) would be of key value to further investigate these issues.
