A stuck thermostat will prevent coolant from circulating through the radiator & heater core.
Incorrect!
The T-Stat is designed to fail in the open position. Spring gets weak and it opens early, result is you don't get up to operating temp.
When the T-Stat is closed coolant circulates thorugh the pump, block and heater core only. This is so the engine heats up quickly. Once it's up to operating temp, the T-Stat opens and lets coolant flow through the radiator.
To the OP. Have and exhaust gas analizer sniff your radiator. It's possible you have a small head gasket leak which shows up when things heat up.
It's also possible that your cooling system is plugged up. Have it completely flushed and check for proper circulation and heat dissipation from your radiator. Being you state your not getting any heat, my guess is a circulation issue. Two things cause that 1) system plugged up, 2) air gets into the system ie. exhaust gases.
The water pump generally doesn't fail to pump as it's a vane type. When it fails, it simply leaks.
Another thing to check is the fan clutch operation. It should have a fair amount of resistance, yet allow the fan to free spin. When the air running across the radiator heats it up it should bind up and spin the cooling fan at near engine speeds to aid in cooling.
Do make sure you use at least a 50/50 mix of antifreeze and water. Premix would be best to top the system off with. The reason is that antifreeze itself is a horrable heat dissipator and needs the water to help it disperse the heat from your engine out through the radiator.