A method is described for the precision measurements of the isobaric heat capacity C-p of hydrocarbons of the normal series in a wide neighborhood of the critical point, characterized by anomalously high values of C-p, the presence of maxima and high temperatures, for which thermal decomposition of the products investigated is possible. Modernization of the method was undertaken in order to increase the accuracy of measurements of the absolute temperatures (the reference temperatures) and small differences in temperature (Delta T < 0.1 K) with original '' ignoble '' thermocouples. In order to minimize heat loss in the calorimeter and to increase the reliability of the experimental equipment, a new construction of the heat meter was developed and a metrological estimate of it was carried out.