if 30 degree air is heated to 110 degrees in the process of being compressed, i don't think the 70 degree isn't going to be heated to to 150 degrees, just because it started off 40 degrees hotter.
also cold air is denser, so when it is compressed it will expand more. this would mean a higher pressue in the intercooler pipe. the wastegate then sees this higher pressure and opens the wastegate further, slowing down the turbo, so it pumps less air.
which means pressure on the air coming out of the wastegate.