Does this sound like a bad thermostat?

First got the "Low Coolant" light 2 days ago

got the light again yesterday and filled it with water

today the heater core went bad and sprayed water/coolant on my passenger side floor. Then I bypassed the hose for the heater. Also filled up the radiator with 30/70 coolant/water and 5 miles later it says "Low Coolant" and it's bone dry with no sign of leaks when i check it out an hour later

We think it's that the thermostat is stuck shut because with the rad. cap off the fluid perculates (sp?). and that that caused the heater core cr@p out. Tomorrow on goes the 180deg tstat- right move?
 
It won't hurt to try a new stat. But the water perculating raises the possibility of maybe a blown head gasket. If the water keeps going low with no visual leaks then where is it going :shrug: . Hopefully the system just had air in it and it burped it self and thats why it was dry but the water perculating could mean ( prey to god that it isn't ) a sign of combustion mixture seeping out hence the head gasket. It hasn't over heated has it?