I would be cool with a diagnostics interface that I use for monitoring, but yeah I don't need my fridge uploading how much chocolate cake I have or the number of beers I drank Saturday night to the cloud where a health insurance risk manager can make assumptions.
Display with temperature, possibly load level (relevant when freezing), beeper for a door alarm and as those two are already there also add a clock and kitchen timer. USB interface in case you want to protocol and control programmatically, no need to have a port just make sure to document where the pins on the board are. Make the display LED for longevity, no need for pixels 4-position alphanumeric is fine. Not blue or at least let me dim the thing.
Oh, and a feature that every refrigerator should have: An oil sensor as the compressor running dry if the thing has been tilted is a sure-fire way to kill those things and hardware shouldn't bloody kill itself just by turning it on.
