@Ionus,
But let's look at your argument in more depth.
You argue that we can't figure out how much heat there is based only on a maximum and minimum. I showed that we can compare how much heat there is based on maximum and minimum.
We know that the average for the day must always be between the maximum and minimum. You do agree with that, don't you?
We also know that for every day if you take readings every hour, that average may not equal the average of just the max/min.
So, if we were to take readings every hour and compare that average to the average for the max/min we would find that there is some relationship that could be shown to exist statistically. We would be able to show that the average of readings every hour has a 95% probability to be within a certain range compared to the average of max/min.
So, let's take readings for 100 days and compare the 2 averages. Now, if we take those 100 readings we can find a formula where 1/2 of the averages by hour are less than the min/max average and 1/2 are more. Surely you would agree with that.
This is what you want to be the day's average - DA
DA = min + max + 23 other readings between min and max (or how many other readings you want to insist)
DAX= (DA1+DA2+DA3...+DAn)/n
would give us the average for n number of days DAX
MMA is the average using only min/max
MMA= (min+max)/2
MMAX = (MMA1+MMA2+MMA3...+MMAn)/n
would again give us the average for n number of days - MMAX
Do you agree that we could write
MMAX + Z = DAX
where Z is some unknown number but could be calculated?