CHICAGO — When city students arrived for the first day of school under the blazing temperatures of a Midwest heat wave, staff greeted them with some unusual school supplies: water bottles, fans and wet towels to drape around their necks.

This year’s late August heat exposed a tug-of-war in districts that are under pressure to start school earlier but are unable to pay to equip aging buildings with air conditioning. Parents are issuing an ultimatum: Make classes cooler or start the year later.

“Thinking about air conditioning — we can’t even afford new textbooks,” said Bement Community Unit School District Superintendent Sheila Greenwood, who oversees a tiny district of 380 students about 20 miles southwest of Champaign, Ill.

As temperatures soared past 90 last week, some Midwest schools gave students extra water and bathroom breaks or canceled after-school activities. Districts from St. Joseph, Mo., and Frankfort, Ind., sent kids home early. In Fargo, N.D., five schools got the week off, and schools in Minneapolis closed down, too.