This work deals with the application of the temperature oscillation method to measure local values of the heat transfer coefficient in laminar flow in a straight horizontal pipe and in a pipe with a bend. This method, applied here for the first time in such experimental conditions, uses a time-varying heat flux as a boundary condition, which is a condition of the third kind. Since an analytical solution for such conditions could not be identified in the existing literature, a numerical study of this problem is applied here. Experimental data for a straight horizontal pipe confirm the numerical results within a reasonable level of error. Experimental measurements on a straight horizontal tube are consistent with predicted results in the literature for both total and local heat transfer coefficient values. The measurements on bent tubes show a very significant influence on the local values compared to the straight tube and in the overall values this change appears as an increase in the heat transfer coefficient.