This paper shows the tolerance of thermal parameters addressed to a building simulation model in relation to the local control of the HVAC system. This work is suitable for a modeler that has to set up a building simulation model. The modeler has to know which parameter needs to be considered carefully and vice-versa which does not need deep investigations. Local differential sensitivity analysis of thermal parameters generates the uncertainty bands for the indoor air. The latter operation is repeated with P, PI and PID local control of the heating system. In conclusion, the local control of a room has a deterministic impact on the tolerance of thermal parameters.