A bad coolant thermostat could be a potential cause of a blown head gasket if the thermostat stays stuck closed and doesn't allow the coolant to flow through the engine properly to cool the engine down.
One common cause of a blown head gasket is due to the engine overheating causing engine cylinder heads to warp which then cracks or breaks the head gasket.
If the thermostat is stuck open it won't cause an overheating issue and will not cause a blown head gasket though but a stuck closed thermostat can overheat an engine and cause a blown head gasket.
Other things that can cause a blown head gasket are a faulty water pump, clogged radiator, coolant leak etc or a non working cooling fan on the engine.