Thermal convection is always present when the temperature of an NMR experiment is different from the ambient one. Most often, it falsifies the value of the diffusion coefficient determined by NMR diffusiometry using a PGSE NMR experiment. In spite of common belief, it acts not only at higher temperatures but also at temperatures lower than in the laboratory. Sodium alkyl-sulfate monomers and micelles in D2O solvent were used as model molecules measured at T = 319 K in order to show that thermal convection sometimes remains hidden in experiments. In this paper, we demonstrate that the increase in apparent diffusion coefficient with increasing diffusion time is a definite indicator of thermal convection. Extrapolation to zero diffusion time can also be used to obtain the real diffusion coefficient, likewise applying the less sensitive pulse sequences designed for flow compensation or the expensive hardware, e.g., sapphire or Shigemi NMR tubes, to decrease the temperature gradient. Further, we show experiments illustrating the effect of a long diffusion time in which the periodic changes of the echo intensity with gradient strength appear as predicted by theories.