I recently bought a 2005 f150 super crew 5.4L and I noticed when I bought it that the heat didn’t work too well and the temp gauge would barely move. I just thought it would be a thermostat and an easy fix so I went ahead and got the truck. Fast forward to tonight when I went to change the thermostat. I went to drain the radiator and nothing came out. Thought it was odd but continued on working and removed the hose on top of the thermostat housing. While removing the hose coolant just started pouring out. I just figured that the thermostat was stuck closed causing the coolant to stay right there. So I removed the old thermostat and the only part I pulled up was the the top of it. The rest of thermostat was not attached. It broke off and I could not find it. I tried digging my fingers down to feel for any piece of it and I couldn’t. And I don’t have a magnet to reach down any further. So am I SOL and going to have to tear apart the coolant system till I find the pieces? Or is there a filter somewhere that would stop it.

Thanks!