A process and apparatus for producing a dimensionally stable melt blown nonwoven fibrous web. The process includes forming a multiplicity of melt blown fibers by passing a molten stream including molecules of at least one thermoplastic semi-crystalline (co)polymer through at least one orifice of a melt-blowing die, subjecting at least a portion of the melt blown fibers to a controlled in-flight heat treatment operation at a temperature below a melting temperature of the at least one thermoplastic semi-crystalline (co)polymer immediately upon exiting from the at least one orifice, and collecting at least some of the melt blown fibers subjected to the controlled in-flight heat treatment operation on a collector to form a non-woven fibrous structure. The nonwoven fibrous structure exhibits a Shrinkage less than a Shrinkage measured on an identically-prepared structure including only fibers not subjected to the controlled in-flight heat treatment operation, and generally less than 15%.