Temperature gradients in liquid-state NMR samples are unavoidable, but undesirable: they lead to sample convection, and consequently to signal attenuation in experiments that use field gradients. This paper illustrates how widely the dependence of sample convection velocity on the temperature at which the sample is maintained can differ between different probes and different spectrometers, including the first such results for cryoprobe systems, and highlights the importance of understanding this dependence if the effects of sample convection are to be kept to an acceptable minimum. It is sometimes thought that efficient sample temperature control should suffice to avoid convection: alas, this is not true, and rapid sample convection can occur even with the best hardware. Previous experiments have shown that the effects of convection can sometimes be avoided by setting the sample temperature regulation to one particular temperature; here it is shown that no such temperature exists in some probes. The issue of convection is all too often swept under the carpet; these results confirm that it is a more general problem than is commonly realized.