PROTIP for folks in the Seattle area: I've had the best luck getting bags of ice at Saar's. https://www.saarssupersaverfoods.com/StoreLocator/State/?State=WA
Unlike the larger/more mainstream grocery stores, they've been a lot better about keeping their ice chest stocked, and also not imposing a ridiculously low limit on customers. I'm not sure how they do it but they've been AMAZING for me while I was still getting my freezer up to ice-making capacity.
Also, if you have any plastic food containers (like big Tupperware bins or the like), fill them up with water and fill your freezer with as many of them as you can. Then you can blow a fan over it to get a small air conditioning area.
Also put damp towels in the freezer as well. Those make very good cold compresses that you can use to chill yourself in a hurry.