Does TMean = (TMax+TMin)/2? I'd say that the answer is generally no.

Is this approach appropriate for your purposes? That depends on what you want to do with the temperature data. Determining whether this approach is "good enough" for you is a question that I can't answer for you. If you have a bunch of dates where you have TMean, TMax, and TMin, why not calculate TMean as the average of TMax and TMin and see if the calculated TMean is close enough to the reported TMean value for whatever you want to do with the data? 

Out of my own curiosity, I took a year of air temperature data, with average temps recorded every 15 minutes, for a station in Virginia (USA) and calculated the daily average as the average temperature of all 360 15-minute periods in a day. I also calculated TMean as the average of the daily min and max temperatures. In the attached file there is a histogram showing the difference between the daily average and the calculated TMean value. For roughly 90% of days, these two values were within ~±1° C of each other. But, there were other days where the difference was much greater (you can probably ignore the really, really large differences; this dataset has not yet been fully QA/QC'd and I suspect outliers). I can imagine that a temperature accuracy of ±1°C would be good enough for some applications but not for others. 

I hope this helps,

- Scott

Not appropriate to have Tmean..when many data are missing..

You should define the case, in terms of missing ratio. In the set if there is sufficient information you may generate a Tmean sampling at random within medians of the real distribution, but this requires a number of complete obs, Refs in R MICE https://www.r-bloggers.com/imputing-missing-data-with-r-mice-package/

Dear Angela Kim,

You can relate Tmean=Tmax+Tmin to calculate the missing Tmean data, but there is a problem with the error of that account. Probably will be a big mistake and data unusable. I suggest that you apply another method for obtaining missing data, such as the interpolation of the Tmean value.

Regards,

Milivoj B. Gavrilov