As it happens, we've been two-three weeks with no fridge at all. It arrived on Wednesday, we cleaned it on Thurday, and by evening it was mostly cold. We don't have much except wine to put in it until we go grocery shopping. (There's no lack of food not requiring cold here though!)
Food advice argues the importance of going shopping for fresh food on a regular basis, ideally several times a week. A daily shop of fresh fruit and veg is even better. I've been going food shopping even more frequently than that: twice daily, at least, once before lunch and once before dinner, with breakfast bars to start the day. It helps that there are three supermarkets within a ten minute walk.
Yet, I'm not sure I've ever gone so long eating so little fresh, thoroughly unprocessed food. The problem is this: with no fridge, there's no point buying any spoilable food that cannot be eaten immediately. No leaving three-quarters of a container of milk for a few hours. No leaving half-a-cheese or an open carton of juice until the next day. No half-an-onion until the day after that. No buying sauces which will keep in the fridge for three weeks.
Most fresh food doesn't come in units which can be comprehensively consumed right away with no leftovers, so we've been living on ready meals and premade salads. So much as I will now be going shopping less than twice a day, now, once again, fridge-enabled, I can return to fresh foods, to cheese and large cartons of juice, and parts of onions and sauces.