What's the actual cause for no cabin heat (pump dead, stuck thermostat?)

I'm more experienced with Gen2 then Gen3 Prius and they changed so many things in stupid ways in Gen3 so it may not apply, but you have an electric heater as well as a heater from the engine coolant. The electric one that is the initial part of the system can have a blown fuse sometimes. Once engine warms up the coolant-based heater takes over.

 

The electric supplemental element is about 700 watts ⇒ scarcely noticeable compared to what you (should) get when the engine is warm (on the order of 5300 watts). About the only way I can ever even tell whether the electric element works or not is that it does get the windshield to defog marginally faster on that kind of morning. Many people probably won't ever notice whether their electric supplement works or not.

The HVAC is one of the systems that got simpler between Gen 2 and Gen 3. Gen 3 got rid of the thermos, coolant control valve, and whole separate electric pump that Gen 2 had. (Gen 3 just uses the engine water pump, which is now electric, so it can run even when the engine stops.)

There's no one "actual cause for no cabin heat" ... you just have to figure out what's the cause in your car and your situation. How did you reach the decision to change the sensor and the water pump? And which sensor are you changing (the one on the cylinder head, or the one in the hose tee)?

At the times when you're noticing no cabin heat, what is the coolant temperature? If you have a scan tool, you could read the temperature from both sensors (in case you're wondering whether one is bad; they're probably not both bad). Without a scan tool, you can fall back to older tricks like feeling hoses. Which ones feel hot?

 

The sensors have a negative temperature coefficient (lower resistance as temperature increases), so a reading of −41 degrees is about the same as an open circuit. Have you noticed anything about the wiring to the sensor?

 

If you're in need of an engine, maybe you shouldn't be throwing money at this heat thing? If you live in Irvine CA, there isn't a real need for heat anymore until winter comes around.