A bypassed heater core is not going to blow cold air in 90 degree heat. It will blow the temp of the outside air. I would check the control head to make sure it is actually switching to heat and that the compressor is off when on heat. Do you have the "A/C" button off?
2003 Chevrolet Tahoe 4X4 5.3
2002 Chevrolet 2500HD 4X4 8.1 - BlackBear Tuned