In general, there is a limiting depth in a drillhole above which the reliability of a single determination of heat flow decreases rapidly with decreasing depth and below which the statistical uncertainty of a heat flow determination does not change perceptibly with increasing depth. This feature has been established empirically for a test case comprising a group of twelve heat flow sites in the Republic of Zambia. The technique consists of constructing heat flow versus depth curves for individual sites by progressively discarding data from the lower part of the hole and recomputing heat flow from the remaining data. For the Zambian test case, the curves converge towards a uniform value of 67 ?? 3 mW m-2 when all available data are used, but values of heat flow calculated for shallow(< 100 m) parts of the same holes range from 45 to 95 mW m-2. The heat flow versus depth curves are enclosed by a perturbation envelope which has an amplitude of 40 mW m-2 at the surface and decreases linearly to the noise level at 190 m. For the test region of Zambia a depth of 170 m is needed to guarantee a heat flow measurement within ?? 10% of the background regional value. It is reasonable to expect that this depth will be shallower in some regions and deeper in others. Features of heat flow perturbation envelopes can be used as quantitative reliability indices for heat flow studies. ?? 1984.