07 cold air when gas engine stops

I have a 07 and wherever the combustion engine stops while at a stoplight, the heater blows cold air. What is causing this!?
This happens at anytime from the time the engine is warm (duh) to until I've arrived at my destination.
No codes, no leaks, coolant levels look good according to the coolant tanks & the "peak under the cap" method & nothing else looks wrong....well, that I'm aware of.
Only maintenance that has been performed on any part of the heat/cooling system is I replaced the Coolant Control Valve (fun times) 1-2 years ago.

 

Yes, air is nice & hot while driving with no change. The heat stops immediately when the combustion engine stops.

I can understand is the idea about a pump not working properly so keeping mind that since I have heat while engine is running, does the Prius also have an old school mechanical water pump and wants engine stops secondary electrical water pump starts? If no, then I'm leaning towards a sensor/relay type failure...I would think.

 

Appreciate the assist guys. I'm 1 arm down for a few weeks but as soon as I figure this out, I'll post my findings.

 

Well, I can't believe it's been Dec 2016 since I posted this issue and guess what, I never delt with the issue since I wasn't around to deal with it! lol SOOOoooo, winter is among us and yup, the problem still exists. RECAP, with the engine at normal operating temp for the East Coast if the ICE (Gas Engine) is at an idle or low cruising speed, there is no or very little heat. As soon as I spin-up the hamsters the heat comes with a vengence or like it should. With all the testing I have performed, here's what else I've found:
1) The "Special Red Sauce" (Toyota Super-Duper Antifreeze) resovio/leves are good.
2) Not sure if there are heater elements anywhere for pre-warming and if so, I havn't tested or don't feel "pre-heat".
3) Circulation pump (in that heart-valve thingy behind Drivers headlight) is running/working. I heat it.
4) No overheating, warnings or any other symptoms or signs of anything other than no heat until you have the ICE reving-up.
5) Temp setting has no effect other than the normal operation. IE: at an idle cold air is cold air no matter what temp you set it at.

Something I did notice is that the Temp regulation system/Senosr doesn't seem to be as effective as I would expect. IE: if I set the temp at 70 it doesn't seem to keep it +/- 2-3 degrees. It's almost if it's the light-switch concept of heat ON or OFF and no middle ground. Is this true for everyone else?

Ok, going to cycle that CHS? / Heart-valve thingy to see if it seems to be hitting any airbubbles. Stand-by for a year! just kidding.

 

UPDATE: After turning off the sun so I could see that AWESOME postioning of the main tank marks (not the small one near the firewall and not the medium one on the drivers side...can this be any more confusing!) and OH YEA and who's the EINSTEIN who put the "F" & "E" marks in such a perfect location!! (UHG). Anyways, that tank was alittle low so I topped it to the "F" mark. All other tanks looked good to go. Also ran the CHS pump and no odd/bubble sounds where noticed.
Took it out for a 12-20 mile trip and upon return, and sitting in the driveway with temp set at 72F, I feel cold air from the vents. Outside temp-like air (48F). Mashed on the "gaser" and here comes the heat!
#CONFUSED!

 

Appoligies andrewclaus I just realised that I never provided any feedback to your suggestion. Let me take a look tommorow and I let you know my findings.