The infalling gas will, in general, be rotating like water around a drain. The rotation leads to a shear (technical word for fluid rubbing against itself), and

The infalling gas will, in general, be rotating like water around a drain. The rotation leads to a shear (technical word for fluid rubbing against itself), and since the gas has non-zero viscosity (technical word for fluid friction coefficient), shear leads to heat production. In the purely non-rotating case, there is another source of heat as well: compression. As gas from far away moves closer to the black hole, the distance between gas molecules decreases, and the pressure increases. This causes the temperature to increase. Just feel the outside of a bicycle pump after quickly inflating two full tires.