Molecules have proved to be extraordinary platforms to test quantum transport mechanisms, with predicted high Seebeck coefficient and thermoelectric efficiency, due to the discreetness of their energy levels and the tunability of their characteristics via a precise control on the chemical synthesis. Those features make molecules interesting systems to be studied as thermoelectric converters or energy harvesting devices. Here we use a break-junction setup based on a Scanning Tunneling Microscope tip in contact with a gold-covered suspended platform, acting as high thermal insulated thermometer (>107 K/W) and high precision heat flux sensor (<10 pW). We show the quantization of the electrical conductance due to the availability of only a finite number of transport channels in the junction, the measurement of molecular thermal conductance with picowatt resolution and the Seebeck coefficient for molecules with the same electrical backbone but different side groups attached to the central backbone. Our work develops a reliable method to characterize transport at the single molecule level and is a step towards the complete measurement of thermoelectric efficiency of molecular junctions. *Funded by the EU Commission H2020-FETOPEN ‘EFINED’ (no 766853 ) and H2020-FETOPEN ‘QuIET’ (no 767187).