As you know, the heating of the pitot tube is to eliminate icing up and impeding airflow to the pitot static system. There is no appreciable density difference in the air flowing through the heated tube. If the air were moving very slowly, you may be able to measure a miniscule density difference and maybe even a very small temperature difference, but at over 100 mph it makes absolutely no difference to aircraft systems.
BTW, The mass of air is proportional to the air density, which is proportional to the absolute pressure and inversely proportional to the absolute temperature. Changes to one will result in changes to others - It's the LAW