We propose observations of the H2 pure rotational transitions
in the ultraluminous galaxies/quasars Arp 220, Mrk 231, FSC10214+4724,
and H1413+117 in order to probe the warm molecular gas content in
these extraordinarily gas-rich systems. In Arp 220 and
Mrk 231, the S0 (28um),S1 (17um), and S3 (9.7um) transitions
will be observed; in the two high redshift systems only the
S1 and S3 lines are proposed. Detection of these transitions
with ISO should be possible if significant fractions (ranging
between 0.0001 and 0.1) of the total molecular gas contents are
at temperatures exceeding 200-400 K. While these conditions would
be very exceptional for the molecular clouds in normal galaxies,
they may not be unreasonable for these rapidly evolving systems
with extraordinarily high radiation densities.  The detection of
the H2 pure rotational transitions with ISO will imply that the gas
in the high luminosity galaxies is much hotter (>200K), requiring
a very critical re-evalution of the mm-wave line analysis.