Refuse incineration slag is fed into a first heating chamber (2) and is melted there under oxidising conditions. Hence the melt is led into a second heating chamber (3) where heavy metal components are reduced into their metallic form, after which the melt is led into a third heating chamber (4). In each chamber the heavy metals present in metallic form are sedimented. The heavy metals sedimented in the third chamber (4) are continuously fed back into one of the preceding chambers (2,3) for collection and withdrawal. The heating chambers are connected to one another by means of passages (17,33). The chambers (3,4) have a bottom sloping towards the chamber (2) which incorporates a heavy-metal collecting pit (11).