The cold high pressure densification technique (CHPD) was recently developed in Geneva for improving the in-field critical current density Jc of in situ binary and alloyed MgB2 wires and tapes,. Jc of CHPD treated square wires alloyed with malic acid (C4H6O5) was enhanced by a factor 2 at 10 T and 4.2 K. In order to understand the fundamental mechanism behind this strong improvement of Jc, the properties of binary and alloyed MgB2 wires have been investigated without and with CHPD, using resistivity and specific heat measurements in the temperature range from 5 to 35 K in magnetic fields up to 15 T. In particular, a deconvolution of the specific heat data was used to determine the distribution of Tc in the samples. We have found that the effect of the densification process on the electrical and transport properties is related to the improved grain connectivity and percolation. By combining the results arising from the analysis of the Tc distribution and those from resistivity measurements, it is concluded that the minimum superconducting volume fraction needed for the percolation of a superconducting path is strongly reduced in samples treated by CHPD.