Well, I wouldn't suggest using tap water for your developer (or really for mixing fixer, stop, and for final rinse). I'd suggest distilled. We have a cartridge undersink water filter in our house, so I often use that fro prewash and stop, but always distilled for developer and final rinse.
I live in Dallas, same deal, bathwater all summer, ice water all winter. I just use a sort of rubbermaid tub with ice water or hot water to get my pre-wash, dev, and stop to 20°c. Sometimes I pour a little distilled into a baggie and freeze it, and I can crumble it and toss some ice chips in the dev if I don't want to wait. My washing temps don't get hot enough for reticulation (and warmer water washes film and paper faster), but it would be simple to cool down a pitcher or two of water, even just toss some ice in a pitcher, fill it with water, and there's a few tanks worth of wash. I've stuck a pitcher of distilled in the fridge or microwaved it and then "mixed to temp" when I want to get to temp faster.
I sometimes do large liquid emulsion prints on canvas, and I coil some tubing up in a cooler with a bag of ice poured around it, and run my wash water through that, as room temp water softens the emulsion too much.