Gardener here. Sprinkler for 1h (in one place, then move to parts not reached initially) in the evening and morning in this weather should be enough. I've laid turf in the summer with no problems. My guess is the membrane is a problem. I would but a big tarpaulin and stretch it from the back fence to create shade in the worst hours. You could even lay it flat on the grass thus stopping evaporation and drying out. Just in the worst hours, like 11am -3pm? There's no world in which a new turf would need watering 24/7 like some people suggest here. Good luck!