The heater core installation is complete, and it works very well. Previously, the air coming through the vents was about 15-20˚ warmer than the outside air (with AC off). This forced me to either open the windows or use the AC. This is because the Yaris uses a wimpy lever to block the heater from the air ducts.
Parts:
Four Seasons 74701 valve - $12
hose clamps - $4
This valve has a vacuum actuator, which is incompatible with the Yaris. It's very difficult to find manual valves in the right size. So I modified this with a hacksaw, leaving a manual actuator lever.
Now the vent air is almost the same temperature as outside, maybe 2-3˚ warmer. And I imagine the engine heats up faster too.