We had some interesting discussions in the past on the calculation of the average temperature (read here and here, I thought it was an interesting re-read).
As a result I created my chart 'Clash of Averages' and below you find the screenshot for the last two months. Why I show this is because the difference between the CMX average and the (Tmax+Tmin)/2 estimator has for the first time in four years reached 4 °C. I find that a lot (normally it is around 1 degree).
For the relevance of this number read the referenced discussions and look into the meaning of Tavg in climate discussions.