  When heated, micro-resonators present a shift of their resonance frequencies.
We study specifically silicon cantilevers heated locally by laser absorption,
and evaluate theoretically and experimentally their temperature profile and its
interplay with the mechanical resonances. We present a enhanced version of our
earlier model [F. Aguilar Sandoval et al., J. Appl. Phys. 117, 234503 (2015)]
including both elasticity and geometry temperature dependency, showing that the
latter can account for 20% of the observed shift for the first flexural mode.
The temperature profile description takes into account thermal clamping
conditions, radiation at high temperature, and lower conductivity than bulk
silicon due to phonon confinement. Thanks to a space-power equivalence in the
heat equation, scanning the heating point along the cantilever directly reveals
the temperature profile. Finally, frequency shift measurement can be used to
infer the temperature field with a few percent precision.
