I turn the heat down on my hot tub in the summer to make it a cool tub, but the night time temperatures are in the seventies, not in the one hundreds like in your situation. All you have to do is get the spa temperature lower than body temperature for it to feel cool.
With your low temperatures being so high, I don't think running the bubbles and jets all night would do it for you. I would try putting block ice in the spa and keep it shaded and covered. Once the spa temperature gets to the low nineties, The spa's insulation should help keep it there and you'll only need to put block ice in it occasionally..