  Thermal lensing in resonant optical interferometers such as those used for
gravitational wave detection is a concern due to the negative impact on control
signals and instrument sensitivity. In this paper we describe a method for
monitoring the thermal state of such interferometers by probing the
higher-order spatial mode resonances of the cavities within them. We
demonstrate the use of this technique to measure changes in the Advanced LIGO
input mode cleaner cavity geometry as a function of input power, and
subsequently infer the optical absorption at the mirror surfaces at the level
of 1 ppm per mirror. We also demonstrate the generation of a useful error
signal for thermal state of the Advanced LIGO power recycling cavity by
continuously tracking the first order spatial mode resonance frequency. Such an
error signal could be used as an input to thermal compensation systems to
maintain the interferometer cavity geometries in the presence of transients in
circulating light power levels, thereby maintaining optimal sensitivity and
maximizing the duty-cycle of the detectors.
