The 808 nm pump diode drifts in wavelength 0.20 nm / Deg C, that is generally not the problem, in fact, depending on the diode, cooling it may shift the wavelength just enough to INCREASE the pump adsorption, depending where it is on the lasing medium's adsorption curve, The KTP frequency doubling crystal is cut using X-ray diffraction for orientation and a cheap one has a roughly +/- 20 degree operating temperature region or the efficacy fades to zero. The phase matching angle (critical for frequency doubling) is very temperature sensitive for type II phase matching. So cooling it detunes the pump diode, but detunes the crystal far worse.
In large lasers we cool the diode, and heat the doubling crystal to an optimal phase matching temperature.
BAD VIDEO.
Steve