Window A/C Remote Temperature Sensor
Is it possible - probably.
Is it practical - probably not. Start with voiding the warranty and work up from there. The odds of ruining the thing so it does not work any more are not insignificant, depending how it's constructed and your personal skills.
Is it far simpler to just set the unit to 66 or 64 degrees, if that's what it takes to get the other room down to 72 - yes.
Can you perhaps assist the process by adding a fan between rooms to help circulate the air - Yes, and that might reduce the amount you have to overcool the first room to get the second room cool enough.