The onset of convection induced by transient heat conduction in deep fluid is examined for two boundary conditions, namely: fixed surface temperature (FST) and linear rate of change of surface temperature with respect to time (LTR). Transient Rayleigh numbers (Ra) for these boundary conditions are defined for each of the respective modes of heat transport. It is found that the onset of convection can be predicted from a maximum transient Ra if its corresponding Blot number (Bi) is known. Hence the critical times and critical depths for stable heat conduction in fluids are obtained. However? the Blot number for an interface in an unsteady-state experiment is difficult to determine. A transient Blot number is defined to allow the evaluation of Bi between Bi = 0 and infinity. The onset of convection for a FST boundary has yet to be verified experimentally, although it has been shown to be valid in analogous gas absorption experiments. The LTR model is found to have no distinct value of Blot number, which could lie between those of CHF (constant heat flux) and FST. The purported LTR experiments were difficult to verify because surface temperature profiles were generally non-linear and the Blot numbers for the system under study could not be determined with certainty. In all cases the critical magnitude of the maximum Rayleigh number for each mode of heat conduction is unique and is independent of the critical time and the depth of the fluid.