The mandrel 104 desirably may be hollowed, as at 118, and provided with a plurality of passages 120 through which air under pressure, water or other fluid may be circulated in order to effect more rapid cooling of the pipe-end 14a after the mandrel 104 has been inserted into the heat-softened pipe-end under compression and such pipe end 14a has been forced out and molded into its desired bell-shap