We proposed the design of a four-layer detection pixel of the single-photon thermoelectric detector with semiconductor FeSb2 sensor. The processes of heat propagation in a detection pixel after the absorption of a photon were studied using computer simulation. The calculations were based on the equation of heat propagation from a limited volume using the three-dimensional matrix method for differential equations. The temporal dependences of the detector signal amplitude were calculated for various thicknesses of the detection pixel’s layers and the following parameters were determined: signal delay, timing jitter, maximum signal value, time to reach the maximum signal, decay time and count rate. It was proved that a detector with such a detection pixel can provide detection efficiency above 95% for near-infrared photons. At the same time, the terahertz count rate was achieved.