If the parts C, R1 and R2 configure the gain of the internal amplifier of sensor, then C reduces this gain to 1 at DC. Only at frequencies above the corner frequency formed by C and R2 the gain is (R1+R2)/R2. By this the internal biasing potential, needed to make the amplifier and the detector work, call it offset, isn't amplified, but only the modulation frequency.

So, of course, your detector gives you a response for DC light, but only provided by a weak gain (gain=1). Only when you use modulated light, you can profit from the higher gain (R1+R2)/R2.

You talked about temperature drift of this offset, when you measure DC light. When you would use modulated light, on the other hand, this offset drift wouldn't play any role, because then you are only interested in the amplitude of this modulated signal. The offset can then be suppressed by an additional high pass filter.

The temperature sensor inside is to compensate for the temperature drift of efficiency of sensor, I guess.

Kai Klaas