Is it acceptable for a forecasting model to predict moving averaged version of the data?
In estimation theory, the simplest way to estimate a random variable is to predict the average of its realizations. Very easy, very simple and very naive to be useful. 

Let me explain more: in your problem which is the weather, the correlation is very high between the data from the last several days and the next day, which makes your estimation a good one but in many problems, the corelation between the data from previous days and the next day is small ( the stock market). Another thing you need to keep in your mind which is the cost of doing a mistake, meaning, predicting the temperature to be the average of the last few days (75), if the actual temperature is 78, then the difference is 3 may be acceptable, in stocks, if the average from the last few days is 10 and the actual value is 10.5. This difference 0.5 may not be acceptable. 

What does mathematically this mean?
If the acceptable error in you estimation is &lt;&lt; than the variation within the data having an average based estimator is not acceptable.

Regarding the issue of transforming the data from one domain to another, it is okay if you a deterministic mapping function that can take you back to the original domain. We prefer to have one to one mapping