Expansion and Contraction: The density of mercury affects how it expands and contracts with temperature changes. A liquid with a consistent and predictable expansion rate is essential for accurate temperature readings.
Calibration: The density of the liquid must be known to calibrate the thermometer accurately. This ensures that the scale on the thermometer corresponds correctly to temperature changes.
Thermal Conductivity: While conductivity can influence how quickly a liquid reaches thermal equilibrium with its surroundings, it is not as critical as density for the overall accuracy of the thermometer.

But in choosing mercury as a thermometric liquid, the density of mercury is not usually considered.