After having struggled for many days with the instability of the ESP (I almost got some code going which read the DS18B20 sensors and upload the reads via the wifi, but the ESP kept resetting or returning unpredictable results) I did some more reading up and found these clever guys are now using the microcontroller on the ESP to do lots more things.
With NodeMcu firmware you can connect the DS18B20 sensors directly to the ESP and run LUA code. No more need for the Arduino and no more AT commands!!!
You can also download this great GUI (ESPlorer) for sending LUA code to the ESP
A day later, no arduino, and I seem to have stable code uploading the results.
This is great! Time to order a few more of these modules!