Heat-transfer coefficients in the form of Stanton number and boundary-layer transition data were obtained from a free-flight test of a 100-inch-long 10° total-angle cone with a 1/16-inch tip radius which penetrated deep into the region of infinite stability of laminar boundary layer over a range of wall-to-local-stream temperature radius and for local Mach numbers from 1.8 to 3.5. Experimental heat-transfer coefficients, obtained at Reynolds numbers up to 160 x 106, were in general somewhat higher than theoretical values. A maximum Reynolds number of transition of only 33 x 106 was obtained. Contrary to theoretical and some other experimental investigations, the transition Reynolds number initially increased while the wall temperature ratio increased at relatively constant Mach number. Further increases in wall temperature ratio were accompanied by a decrease in transition Reynolds number. Increasing transition Reynolds number with increasing Mach number was also indicated at a relatively constant wall temperature ratio.