  We propose that the mass-temperature relation of galaxy clusters is a prime
candidate for testing gravity theories beyond Einstein's general relativity,
for modified gravity models with universal coupling between matter and the
scalar field. For non-universally coupled models we discover that the impact of
modified gravity can remain hidden from the mass-temperature relation. Using
cosmological simulations, we find that in modified gravity the mass-temperature
relation varies significantly from the standard gravity prediction of $M
\propto T^{1.73}$. To be specific, for symmetron models with a coupling factor
of $\beta=1$ we find a lower limit to the power law as $M\propto T^{1.6}$; and
for f(R) gravity we compute predictions based on the model parameters. We show
that the mass-temperature relation, for screened modified gravities, is
significantly different from that of standard gravity for the less massive and
colder galaxy clusters, while being indistinguishable from Einstein's gravity
at massive, hot galaxy clusters. We further investigate the mass-temperature
relation for other mass estimates than the thermal mass estimate, and discover
that the gas mass-temperature results show an even more significant deviations
from Einstein's gravity than the thermal mass-temperature.
