To corroborate what EdStainless has said, here is a table from the literature showing some values:
HV Hardness Thermal cond.
kg/mm2 W/(mK)
Plain CS low strength 140 16
Ditto high strength 220 25
LCS hardened AISI 4340 560 42
Martenisitic (Cr-Ni) 630 (17-4 PH) 470 17
Austenitic (Cr-Ni) AISI 304 160 16
AISI 316 160 16
Tool steel M-2 Hardened (830-930) 21.3