TMean as supplied by Environment Canada is simply (TMax+TMin)/2. That is, it's the half way point between the highest temp and the lowest temp of the day. If the hourly temperature profile were a perfect sine wave this would not be a problem. But the hourly temperatures are not a perfect sine wave. Far from it.
In a perfect sine wave the average of all the hourly temps and the TMean would be the same. But because the daily temperature trek is not a perfect sine wave the hourly average is not the same as the TMean. TMean could be more than the hourly average, it could be less. The point being the hourly average is a number that is closer to what is physically going on. TMean is not.
I download the hourly temp data for the month of November, 2010 for Station 4333 so you can see the difference. (For those who think I cherry pick, choose any station, any month, any days you want, you will see the same problem.)
This is the temperature profile for Nov 1 to 4:
Notice TMean is more than the average, substantially more. Thus using TMean as an indicator of how much the planet is heating up is grossly overstating the case for these days at least.
This graph for the entire month of Nov shows the TMax, TMin, average and TMean. Notice TMean is mostly higher than the average:
You can see a slight change in the hourly temperature profile can dramatically change the average, but not the TMean because TMax and TMin have not changed.