Car is overheating but when I turn fan on it only blows cold air?

This is a 2003 Honda Civic with about 140k on it. I've had this car checked out by a mechianic and the thermostat was replaced had a pressure test to check for air pockets, nothing. Had a test for a bad head gasket with some sort of chemical test which came back negative. But the car still overheats. I was told by this mechanic that there's a pinhole sized leak in the head gasket somewhere that leaks into the engine very slowly. I have to drive about 60mi everyday and as I drive at high speeds the car is fine it doesn't overheat. It's only when I'm at idle or driving slowly that the gauge begins the rise. On these daily trips I have the heater blowing the entire time because I know it acts like another fan to take heat off the engine. But when I'm at a redlight all the sudden the air which is on the hot position will turn cold and then the gauge will start to climb. Is this normal for a blown head gasket? Or when the coolant gets low. By the time I get to my destination is the coolant is basically gone and it's about the same time I'm close to my destination that the air turns from hot to cold and overheats. Please any ideas would be fantastic!

Faulty thermostat. It may be brand new but it happens. At low rpms it sticks not allowing coolant to flow through thus overheating and no coolant making it to the heater core

A bad water-pump impeller warn down so it barely pushes the coolant. The heater should be hot as a pistol if the engine is overheating and the thermostat is sticking. The thermostat has nothing to do with the bypass hose water circuit that pumps regardless of the thermostat being open or closed. It sounds like a pump, if it has a radiator cap I would be looking for good strong water flow through the radiator at idle when it's hot with the radiator cap off while revving the engine throttle and you should clearly see the thermostat cycling open and closed by the flow through the radiator core.

Add, how can it be blowing all the fluid if it passes a pressure test. There's a leak somewhere, probably on the side tank of the radiator at the crimp seal that only leaks when it's hot. Drive it until it's hot and pull over off the freeway to inspect it for leaks while the cooling system is hot, full, and under pressure before the coolant has a chance to escape. A pin hole doesn't blow 2-3 gallons of coolant out that fast.

The loss of coolant is the key here. It's either an exterior leak or head gasket.

Certainly sounds like your problem is lack of coolant flow, being a 2003 your radiator and or heater core are corroded thus restricting coolant flow. Can you confirm that the water pump was changed when the timing chain was changed at around 100,000 miles.