The 2 biggest constraints I found were power and communication from within the freezer.
One promising approach was - a BLE enabled temp. sensor beacon with a coin lion battery - a nearby externally mounted unit (RaspberryPi) plugged into a wall socket as a relay - a small central 'black box' SSD/Wifi/router ground-station to collect, store and push the data to the internet
The biggest question was whether the beacon signal could get through the freezer walls. If not then I was going to look into the idea of some super flat cable to enable a wired sensor connection without compromising the freezer seal (like a meat thermometer in an oven)