A study was conducted on gas filtration and heat exchange in a fixed-bed heat exchanger-filter (FHEF) where we have removed fine dust particles from gases and exchanged heat with the granular medium (Lapilli). The influence of a number of variables was examined including gas velocities, gas temperatures, concentration of dust, height of the FHEF, dust and granular mean size, and pressure drop. The collection efficiency was found to decrease with increasing temperature, and the pressure drop increases when the size of the granular medium decreases. A numerical model for gas filtration and heat exchange using the finite element method was developed. It predicts the two-dimensional transient response of both solid and fluid phases as well as the variation of the specific deposit and void fraction of the FHEF with time. The numerical model incorporates variation in void fraction, specific surface area of the medium, and transport coefficient because of the combined processes of filtration and heat exchange.