Accuracy of MWD temperature readings

I am wondering about the temperature readings from the MWD. We are experiencing rather high losses and so we are pumping essentially fresh water as fast as we can.
This is cooling the MWD as is reflected in the temperature reading being sent up.
Is there any way of (at least roughly) adjusting the MWD readings to compensate for the environment??
This got me thinking of even in normal drilling is there any way, (instead of taking time to do a static reading) of adjusting dynamic readings.

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