  Resonant second harmonic generation between 1550 nm and 775 nm with outside
efficiency $> 4.4\times10^{-4}\, \text{mW}^{-1}$ is demonstrated in a gallium
phosphide microdisk cavity supporting high-$Q$ modes at visible ($Q \sim 10^4$)
and infrared ($Q \sim 10^5$) wavelengths. The double resonance condition was
satisfied through intracavity photothermal temperature tuning using $\sim
360\,\mu$W of 1550 nm light input to a fiber taper and resonantly coupled to
the microdisk. Above this pump power efficiency was observed to decrease. The
observed behavior is consistent with a simple model for thermal tuning of the
double resonance condition.
