What kind of model should I use to express temperature change in my experiment?

[TSN79]

For a normal population growth we have the basic equation

$${{dP} \over {dt}} = kP$$

I'm not investigating pop.growth, but temperature change, but it really shouldn't matter if I'm measuring degrees instead of people. The only problem I have is that this equation only seems to be fairly accurate if there is a general increase in the values as it goes along. In my experiment a room is heated for 24h, and I want to express the temperature change using the following set of equations:

$$Q_P + \rho \cdot C_{P,Air} \cdot \dot V\left( {T_O - T_R } \right) = U \cdot A\left( {T_R - T_O } \right)$$

and

$$m \cdot C_{P,wall} \cdot {{dT_m } \over {dt}} = U \cdot A\left( {T_R - T_m } \right)$$

I haven't done the experiment yet, but I'm not convinced that the temperature will always increase steadily, it might decrease in periods, and increase in others. What kind of model should I then use?

Of course, if the temperature does indeed turn out to only have a slow steady increase and no decrease, then there won't be a problem.

 

[Emieno]

That way of solving your current problem complicates everything, I suggest statistical analysis to then predict the changes in temperature instead. By the way, a dot on the V's head doesn't look right to me.