# Calculating outside temperature based on indoor measurements

If I take three consecutive measurements $T_0$, $T_1$, $T_2$ at equal intervals, I can end up with two (Newton’s law of cooling) equations where the $e^{-kt}$ term is the same.

$$T_{n+1} = T_{outside} + (T_n - T_{outside}) × e^{-kt}.$$

So, without knowing the temperature constant of the building, can I calculate the outside temperature?

$$T_{outside} = \dfrac{T_0 × T_2 - T_1^2}{T_2 + T_0 - 2T_1}.$$

Have I missed something? Or is this really possible? (Provided no other sources of cooling and heating)

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To clarify, to measure outside temperature indoor you mean to open the door for a consistent period of time, let the heat out, then close the door, wait for thermal equilibrium across the volume of the house, then measure and repeat? – theUg Dec 11 '12 at 1:05
@theUg no, just measure temperature inside the house with no heating or cooling on. I'm assuming a less than perfectly insulated house. Or does that mean the newtonian equation is assuming perfect exchange? – MandoMando Dec 11 '12 at 3:24