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It is known that the results of calculations for various criterial models of convective heat transfer may differ from each other, which, according to existing ideas, is usually associated with different operating conditions of the heat exchangers under study. In the work, thermal engineering experiments are carried out with a laboratory water-to-water tubular heat exchanger of the “pipe-in-pipe” type with smooth tubes at normal pressure and moderate temperatures at various inlet temperatures of the heat carriers and their flow rates. The results of the experiment are compared with the results of calculations based on the models of B.S. Petukhova, S.S. Kutateladze, Nusselt, and M.A. Mikheev. The comparison shows that the discrepancies between the experiment and the models, as well as between the models themselves, stem not only from experimental inaccuracies, but also from inaccuracies in the models themselves.