chrishennig, any independent shop can complete this work in a short amount of time. I'm no expert here, but the "book time" on this should be an hour or less.
andrewclaus, the Matrix and Corolla have a different heater blowers, and different connectors.
Changing the connector is a pretty straight forward job. The "connector kit" is the wire with the connector and insulated crimp connectors for around $12 + shipping here
https://www.rockauto.com/en/moreinfo.ph ... 60&jsn=421
1. Disconnect the negative battery terminal from the battery
2. Unplug the connector from the blower motor
3. Look at the new and old connector\cables, and note the orientation of the connectors, so when you connect them back up the power flows in the right direction.
4. Line up the new wire with the existing wire (leave an extra inch for trimming the plastic back), and cut the old wire connector off.
5. Use a set of wire strippers
https://www.amazon.com/dp/B07G2WCN2W/ and strip the ends of all four wires.
6. Use the wire strippers to crimp the wires back together, keeping step 4 in mind.
7. Plug the new connector back in to the blower
8. Connect the battery.
9. Test