An aqueous quenching medium for hardening metals by heat treatment contains a solution of 0.1 to 30% by weight of a polyether compound having a molecular weight of more than 5000 and additionally 0.1 to 30% by weight of an at least partially hydrolysed alkali metal metaphosphate and/or of an oligomeric alkali metal phosphate. Only a very labile vapour skin phase or virtually none at all forms in these quenching media when heated metals are cooled.