Not understanding the 328 (308 as well?) cooling system...

I've been elbow deep in the cooling system of my 308 for the past two months and the way I understand it is that is a bleeder hose and it kind of does two things. First it will purge any air in the system (up to a point at least) and secondly it causes the coolant in the expansion tank to circulate which is needed because there are two thermal sensors on the tank. In regards to air my engine has a bad head gasket so it was constantly getting in and despite much of it going through that bleeder line when the thermostat opened some of it would go to the radiator where it gets trapped. If you are constantly seeing bubbles in that stream then there is a problem somewhere but if it turns into a steady stream of coolant you're good.

 

It's more accurate to say that it circulates coolant "up" into the expansion tank. The level in the expansion tank is the highest point in the cooling system (so any air collects there). The injected cars do tend to put various sensors/devices on the expansion tank to sense the coolant temperature as kcabpilot mentioned, but having the expansion tank level above the engine is still important for the (sensorless) carbed cars - the 308GT4 WSM has a decent figure.
At cold start-up, the coolant is just recirculating in the engine (less losses) so the flow would be more forceful in that condition. Once the thermostat valve changes state, there will be more flow losses in the long pipes and radiator (so the pressure at the fitting supplying the expansion tank will be lower).

 

The "hot" coolant going to the expansion tank comes from the fitting on the hot water crossover pipe on a 328 -- hose 49 on Table 22 is the same hose as hose 42 on Table 21.

 

Yes, coolant is pumped into the block then up through the heads and to that crossover manifold which connects to the thermostat that directs it back to the engine or to the radiator or both depending on what state it is in. The small line to the tank comes right off that manifold. and there is going to be some air bubbles when you first start because the output of that line is above the coolant level in the tank. Like I said I've been all through this and have replaced every hose and component in a quest to solve my issue (I started a thread titled "air in the cooling system") In my opinion, when all is right, the system is perfectly adequate and you should have no troubles. The only modification I think might be worthwhile would be to run a bleed line from the radiator back to the tank but the more I think of it the more convinced I am that it's not really necessary.

 

I have a Euro 328 so it may have less "stuff" on the expansion tank. As others have alluded to, the tank is not just an expansion tank but a re-circulation tank. The Auxiliary Air Valve is mounted to the bottom of the tank. The combination of the coolant heat transferring to the bi-metallic "shutter" in the Auxiliary Air Valve, along with the 12 volt heating element in the valve, are what help determine the idle speed with a cold/cool engine.