I would say that this solution provides you an approximated estemation of the carbon intensity. However, CO2 is emitted by the primary energy use; between the primary energy use and the load satisfaction there may be many steps, each one having its own efficiency. Therefore, you could improve the emission estimates using a global efficiency.
E.g., 10 kWh_th/(m^2 * a) * y (kWh_th/kWh_f) * CO2 coeff. (kg/kWh_f) = X (kg/(m^2 *a))
th = thermal (kWh of heat)
f = fuel (kWh of chemical energy the the fuel can release as heat, or otehr definitions of primary energy for non-fuel resourses as solar thermal)
I assume "a" is a time unit.
Moreover, this result represents direct CO2 emissions resulting from load satisfaction. If you want to consider the global emissions resulting from load-satisfaction, and compare significantly different resourses (e.g., natural gas, biomethane, solar thermal, electric heating from different electricity sources) you may need a full LCA analysis.
In the Heat load eqn MCp ΔT , Cp varies with temperature ie 0.79-1.476 to 175 K- 6000K and emission is dependent on the molecular weight conversion of C to its oxidative forms ie direct CO2 and CO, CO to CO2.For CO2 it arrived from both C and CO . So, the light variations should be considered.