  We investigate that temperature can be measured by a modified Michelson
interferometer, where at least one reflected mirror is replaced by a
thermalized sample. Both of two mirrors replaced by the corresponding two
thermalized samples can help to approximatively improve the resolution of
temperature up to twice than only one mirror replaced by a thermalized sample.
For further improving the precision, a nonlinear medium can be employed. The
Michelson interferometer is embedded in a gas displaying Kerr nonlinearity. We
obtain the analytical equations and numerically calculate the precision with
parameters within the reach of current technology, proving that the precision
of temperature can be greatly enhanced by using a nonlinear medium. Our results
show that one can create an accurate thermometer by measuring the photons in
the Michelson interferometer, with no need for directly measuring the
population of thermalized sample.
