98 Dodge Dakota Sport - Heater Core?

V6 model.

Odo is just shy of 100k. We're planning a party.

When I crank the heat for the morning commute, I'll get heat for a little while--say, 20 minutes--when my temp gauge will ramp up to near the redzone over a couple minutes. At that point, I lose heat (air still blows, but it's cool). When I turn my heater off, the gauge settles back to normal operating temp.

I haven't noticed any fluid leaks inside the cabin, so I don't think the heater core itself is leaking. I have noticed some external leaking, but previously figured it to be condensate--tomorrow if I notice any puddles I'm going to give it a whiff.

Any ideas on what to check? Could it be a partial blockage within the heater core? Or could it be my thermostat needs replacing?

If I do end up needing to replace the heater core, am I going to need to discharge the AC system in this make/model?

Thanks in advance!