Welcome to the MySensors community @dj_janker
Yes, what you are describing should be fairly straightforward. You could use the receive() function on the gateway to write to the SD card. I would however use 3.3V Pro Mini instead of Nano for the battery powered nodes. See https://www.mysensors.org/build/battery for more information.
For the DS18B20 see https://www.mysensors.org/build/temp