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 hasn't over heated and there is no sign of oil/water/coolant mixture so i don't think it is the blown head gasket which would be very bad

thanks for the feedback, were pretty sure its the tstat, no harm in checkin