Improved burner constructions for gas-fired infra-red generators having ceramic fiber matrix through the thickness of which gaseous combustion mixture is passed and as it emerges it is burned to heat emerging surface to incandescence. Burner matrix can be loaded with silicon carbide particles to improve its emissivity, can be made water repellent and its uniformity can be improved. Burner body can be casting, with sheet metal addition to form a baffle and air seal and to grip matrix edges. Combustion mixture plenum can have movable partition assembly separating it from air seals, to adjust portion of matrix at which incandescence is generated. Metal screen can be stretched in front of incandescent surface to assist with low-temperature operation. Large size matrix can have central support fitted and secured to back of burner body. Air seal can be provided by narrow curtain of air extending around internal faces of burner body. Annealing lehr is desirably provided with gas-fired infra-red irradiation, and can have heat losses reduced by diminishing amount of metal used as in a conveyor to move workpieces through.