I've got a leak somewhere in my cooling system so I just went out to top it off and refill the coolant reservoir. I ran the engine for a while and made sure that the car was on an upward incline (i.e. as though it were climbing a hill). I noticed air bubbles running into coolant reservoir tank--presumably the air that was still in the system from when the coolant level was slightly low.

If I bring the engine to operating temperature and then let it cool, will the coolant from the reservoir get sucked into the cooling system to eliminate any air pockets?

Thanks.

 

Yes; as long as your system has no leaks. That's exactly how it's designed to work. If there's leaks of any significant size, it will suck air in, instead of the coolant in the bottle.

The most common "mystery leak" is the water pump seal. When they go bad, water leaks out through the bearing, around the shaft, and is slung everywhere by the pulley so you basically never see it. But sooner or later the bearing goes bad because of the water, and usually makes a bunch of noise in the process. So if there seems to be alot of scratchy growling kind of noise coming from the front of your motor, AND a mystery leak, change the pump NOW before it leaves you sitting by the side of the road.