Will borosilicate glass absorb 808nm laser light? If it instead refracts, then what is the refractive index? Also, will borosilicate reflect lower frequencies of light like those used in non contact temp. measurements?
Borosilicate glasses are a family that has many members with differing properties. You can look up the provider for your glass, and check whether it is transparent in the near infrared. I think it would be in most cases (see here for one example).
Unless doped, glasses are effectively 100% transparent in visible and near ir but not usually below approx 300nm in uv. The amount of reflection depends on the polarisation and angle of incidence, look up Brewster angles and Fresnel equations. Refractive index depends on wavelength, (greater at shorter wavelengths in visible region) usually we use the Sellmeier equations to predict this if a value at exactly the wavelength you want is not available.