Is it useful to cool down pyroelectric detectors for example by using a Peltier device to improve the signal-to-noise-ratio?

No. Pyroelectric detectors unlike PbS or PbSe detectors do not need any cooling even for the detection of longwave radiation in the range of 8-14 m. But operating temperatures of over 50 C do however increase the detector noise, as the integrated amplifier components exhibit larger leakage currents at higher temperatures.

It is noteworthy that CMOS OpAmps react much less as JFET's, as the gate leakage current of a JFET increases exponentially with temperature. For applications with operating temperatures above 60C always consider the use of detectors with CMOS operational amplifiers. More.

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