You can try to flush out the heater core to see if it'll help but there's a good chance the air temp blend door or motor is not working properly. The blend door separates heat/cold from the core. On newer TJs like yours, I believe the blend door is motor driven. Motor may be out and the door is stuck on cold.
You should be able to see the small motor. Take the motor off and turn on your heater controls to see if the motor turns when you play with the temp control. If not, replace the motor. If it's good see if you can manually turn the blend door(pliers?). It should not turn freely but have a stopping point either direction. Hope its the motor because I think the blend door replacement is quite involved. Good luck..
Both heater hoses might be hot strictly from how they are routed in the engine compartment. Whenever the TJ's heater doesn't work, my first suspicion is that the heater core is clogged which is usually easily fixed by first flushing the core in a direction backward to its normal flow. Then back & forth after the inital flush.
Gone wheeling, back late sunday... Remember that having a different opinion doesn't also require one to be a jerk when expressing it.
I agree with Jerry 200% = (as the same thing was wrong with mine) - - when I flushed - I used some CLR and water - (but only after flushing with water and compressed air first) and let it soak for a while (20 min) then flushed again using both fresh water and air pressure