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A simple method is proposed whereby the formulas for the transient conductor-temperature rise above ambient of a buried cable, following the application of a constant load, may be modified in order to take account of the variation of the electrical resistivity of the conductor with temperature during the transient. The result is an upper bound for the conductor transient that is more accurate than existing formulas, although the temperature differences involved are not large. A technique is given for obtaining arbitrarily close upper and lower bounds. The method is of more general applicability than the field of thermal transients in buried cables.