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It sounds like your plantsIt sounds like your plants succumbed to the heat. Potatoes are extremely sensitive to high temperature and dry soil, among other things. One source estimated that one potato plant's total water consumption in a season is about 26 inches (over several months) for plants in the ground. Plants in pots—no matter what they are—tend to require more water than those in the ground simply because the soil in the pot, being exposed on the sides, dries out quicker than ground soil. You could trim them and see what happens. (BTW, while you were 88°F in January, we were probably -18°F!)

2015 Special Edition Garden GuideCooking Fresh with The Old Farmer's AlmanacThe Almanac Monthly Digital MagazineWhat the heck is a Garden Hod?