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Underground workings in Witwatersrand gold mines are likely to exceed depths of 4000 in. An important consideration in planning of deep mining is the refrigeration cost which depends on rock temperatures. Temperature measurements made during the past 50 years have resulted in a know-ledge of regional rock temperature variations (Jones and Bottomley, 1986; Jones, 1988), but the temperature structure of most goldfields is not well determined. Temperatures may be predicted using one-dimensional (vertical.) analysis where strata are horizontal, but structural complexities involving rocks of different thermal conductivity and radioactive heat production may result in non-vertical heat conduction. This paper discusses a numerical<br>technique that permits computation of the temperature field in such areas.