For a physicist the most compelling argument for Celsius is its easy translation into Kelvin, the SI unit for temperature. Celsius and Kelvin share the scale, i.e. the temperature difference of 1˚ Celsius and 1 Kelvin is the same, and with Kelvin starting at absolute zero this is -273,15˚ Celsius. So it is T(˚Celsius) = T(Kelvin) - 273.15.

By differing just in the position of the zero value on the scale both Celsius and Kelvin share the precise definition of temperature, which does not rely on water freezing or boiling (which both depends on atmosphere pressure) or people feeling good: it is defined through the Boltzmann constant k (one of the defining constants of the SI system), as a temperature change of 1 K or 1 Celsius degree is defined as the change in temperature of a medium caused by adding the specific amount of thermal energy 0. 5 k * 1 K to each particle and degree of freedom in it.

You can easily calculate the amount of energy (und thus cost) you need to increase the room temperature by 1˚Celsius, you just need the volume of the room, the Avogadro constant, the Boltzman constant k and the pressure (in N/m² - what did you expect?). The ideal gas law does the rest. Child's play :)