Heat is always "on", the antifreeze always circulates through the heater core. What regulates the heat are dampers that open/close depending on the climate control settings. Turning on the AC via the console switch does not turn off the heat, the switch just allows the AC to turn on. Dampers control the amount of cold air to be circulated.

So, you either have a broken damper or a misguided climate control unit.

In my Volvos, I have always left the AC switched on year round and let the climate control regulate the temperature automatically.

As for the check engine light, read the codes.
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Keeping it running is better than buying new