It sounds like you are really between a rock and a hard place.

If it were me...

If planted outdoors, I would put them into pots in the shade - and keep them there until the weather is much more temperate than 90 degrees. In fact, keep them in the shaded pots until late summer/early fall (when it is cooler and will *stay* cooler) - and then plant them in their final location.

If kept indoors, put them in a bucket with some water to cover their roots BUT NOT THE CROWNS. (Adding some Vitamin B1 transplant solution to the water will be helpful, too.) If you don't have enough buckets (or unused kitty-litter tubs), you can improvise by putting one of those very large (XL size, I think) Ziploc bags into a 3-5 gallon pot; the pot provides the shape/rigidity, the Ziploc bag holds the water/solution.

(FWIW, I have several new daylilies out in the garden right now, with the high temp ~ 90. All of them are in the shade, or at worst get a few hours of sun a day. Some of them are in pots (which may get part sun); the rest are soaking in the shade, in kitty-litter tubs or Ziploc bag/pot combos. At these temps, I think that the plants are much better off in the pots; I really should hurry to get them planted...)

I got seven new ones during the peak of our heat, and following the expert advice I received, planted them in pots placed in the shade as Polymerous has suggested. They are growing and doing well. I will plant them a bit later when the worst of summer is over.
kay

Thanks for the suggestions, Polymerous and Kay --
I'll pot them up and put them in the shade before it gets hot today--which means before about 9:30 in the morning.

Kay