A method for making a bonded nonwoven fibrous web comprising 1) providing a nonwoven fibrous web that comprises oriented semicrystalline polymeric fibers, and 2) subjecting the web to a controlled heating and quenching operation that includes a) forcefully passing through the web a fluid heated to at least the onset melting temperature of said polymeric material for a time too short to wholly melt the fibers, and b) immediately quenching the web by forcefully passing through the web a fluid at a temperature at least 50° C. less than the Nominal Melting Point of the material of the fibers. The fibers of the treated web generally have i) an amorphous-characterized phase that exhibits repeatable softening (making the fibers softenable) and ii) a crystallite-characterized phase that reinforces the fiber structure during softening of the amorphous-characterized phase, whereby the fibers may be autogenously bonded while retaining orientation and fiber structure. Apparatus for carrying out the method can comprise 1) a conveyor for conveying a web to be treated, 2) a heater mounted adjacent a first side of the conveyor and comprising a) a chamber having a wall that faces the web, b) one or more conduits through which a heated gas can be introduced into the chamber under pressure and c) a slot in said chamber wall through which heated gas flows from the chamber onto a web on the conveyor, 3) a source of quenching gas downweb from the heater on the first side of the conveyor, the quenching gas having a temperature substantially less than that of the heated gas, 4) gas-withdrawal mean disposed on the second side of the conveyor opposite from the heater, the gas-withdrawal means having a portion in alignment with the slot so as to draw heated gas from the slot through the web and also a portion downweb from the slot in alignment with the source of quenching gas so as to draw the quenching gas through the web to quench the web. Flow restrictor means is preferably disposed on the second side of the conveyor in the path of at least one of the heated gas and the quenching gas so as to even the distribution of the gas through the web.