The present invention describes a stylet that softens dramatically upon insertion into a living body with a temperature of about 37.degree. C. The stylet has a distal end and a proximal end. Upon insertion of the distal end into a living body, the distal end softens from a stiffness of about 78 Durometer Shore D units to 25 Durometer Shore D units in a preferred embodiment. Moreover, the proximal end of the stylet, which is not inserted into the living body, retains its stiffness to aid a physician or a nurse in inserting and placing the catheter and stylet assembly.