Thermopile temperature sensor (non-contact) amplifier design
Some opamps have noise density of 1nanovolt/rootHertz (thus an internal Rnoise of 62 ohms). In 1Hz bandwidth, you'll have ReferredToInput noise of 1nV rms from that internal-to-opamp source. Various gain-set resistors add their own random KT Johnson noise. In 10Hz BW, expect sqrt(10) = 3.16 more noise RMS.
In 100Hz BW, expect sqrt(100) = 10x more noise RMS. The low-noise opamps will be bipolar, and require some input bias currents; CMOS opamps also require input bias currents, but 10^6 or 10^8 smaller levels at least at room temperature. 

I used SCE to examine suitable topology: 5 millivolt, 50 ohm Rsource for the sensor; 1nanovolt/rtHz (62 ohm Rnoise) opamp with Gainset R of 101 ohm and 10Kohm; 160 Ohm/1uF {10Hz} discrete RC LowPassFilter; edited the ADC params to provide 18 bits resolution to drop Quantization stepsize.

Result? 13.5 bits ENOB, set by the random errors; see lower left of screenshot.