Probably wilt dug now, but you can try it anyway. With hot weather on the horizon timing is just about the least suitable. If they don't make it try again in fall or winter.

I planted some raspberries in an area I was advised to get them out of, so I did, in the middle of last summer. The canes died back a bit, but are doing well and putting on good growth this summer.

Its better in this climate to transplant in the winter, but any time will do if you water.