On most "modern" vehicles (at least since the late 70's) there is a box in the back of the engine compartment/behind the dash with 2 compartments. One contains the heater core, one contains the evaporator. The coolant is ALWAYS running through the heater core, as long as the engine is running, unless there is a divert-er valve in the system) The outside air enters the "un-conditioned" side of the box, there is a blend door that is used to direct the air to the heater core, and/or the evaporator core. In a manual system, this is controlled by either a cable (some of the older trucks are this way) and most now are controlled by vacuum (the hiss you hear when you change the temp, or the register (floor, vent, defrost) when the vehicle is not running. The automatic systems are similar but the HVAC control unit controls the vacuum motors, rather than the position of the knob.
Now, on yours, if the control unit is commanding the blend door to stay at 50% equally hot and cold, or the blend door is broken, stuck, missing, bad seal, abducted by aliens...... whatever. The selected temp may read 60 (which if I remember how mine works, it's not my daily driver) 60 is the same as Max, High Fan in a manual system (penguin mode, they way I keep my P71). So the HVAC unit is trying to freeze you out. But, if the blend door can't blend for what ever reason, the fan will be running "balls to the wall" trying to bring the temperature down to 60. But in this situation, the heater would also be running wide open. In just about every case, heat will win over cold. You live in the North, you can heat a room with a 1500 watt (5100 BTU) heater, but it takes a 8000 BTU to A/C to try to cool the same room.
So with the current weather (Here in Central Indiana, we've been running almost 90 with high humidity) you have a little cool, being overrun by 200 degree heater water, along with the 90 degree ambient temperature, the heat is going to win. I would look into the operation of the blend door. There is a laundry list of things that can cause issue (like listed above) or even a pen/pencil that's fallen through the defroster registers........ When it works, maybe you've hit a bump and the pen moved, and wala.... blend door works, then it moves again and cause a jam, or a split vacuum line, or the electronics have gone haywire..... time to start some detective work. You may be able to remove the fan from HVAC Box under the hood and see inside the box........