The thermostat controller for an air‐conditioning system is usually placed in a position at some distance from the unit and this can lead to large swings in temperature. This paper addresses this question by studying a paradigm—a one‐dimensional heat conduction equation with and without heat loss, and where the flux of heat extracted or input by the unit is considered to be a function of the temperature at the other end.

The essential results are that the system can be unstable and that this is exacerbated both by a more powerful air‐conditioning unit and by more efficient insulation.

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