Thanks for the clarification. Now let's think. If the crystals are in a common holder then the temperature requirements will be determined by the LBO as opposed to the vanadate or YAG. If I was the manufacturer then I would set the alignment of the LBO so that it needed to operate at a convenient point above ambient. This way I could avoid the need to cool as well as heat. The whole purpose for adjusting the operating temperature of the NL crystal is to match the temperature to the set alignment angle. This is a a tightly coupled relationship.
If you know the cross section of the entry face of the gain crystal, you can get another diode with or without a FAC and use macroscopic optics to adjust the 808nm beam to match this dimension at a known distance. Do this on the bench, independently of the laser. Optimally, you would want the pump beam to focus down somewhat smaller than the crystal cross section and place this focus slightly past the entrance into the crystal. "><". I would start at about 100mW pump power and slew the crystal assembly from RT up to about 50 degrees C. If nothing, then I would keep doubling the pump power and re-slew the crystal until your up to about 2 W. Assuming you have some blue by this time, you're definitely in the rabbit hole and you can adjust the macroscopic optics to compensate for the thermal lensing and the refractive focus shift caused by the crystal material until you have maximized output.