1999, Cherokee.

On a 70 degree day, I get 90+ degrees from the vent with the temp control all the way on cold, A/C OFF.
My guess is that the blend door is not fully closing, ( assuming this is a blend door system). The heat control is electrical not mechanical or vacuum.

Other than simply pinching off, or re-routing the heater hoses, how can I fix this?

 

Hmmmmm....turn it off and roll down your windows?

 

Not sure about my 99 but on my 94 when you turn the heat on/off I can hear the door closing and opening. You could get some one to turn it on/off while listening for the door in the pass. floor board.

 

Its a jeep.....Good luck.
Mine does the same. guess I use the window trick.