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So why did it overheat? A thermostat isn't the only possible cause of an overheat.
Where is the coolant going? There should be evidence somewhere. A gallon of liquid is a buttload of coolant to lose with zero evidence. (Are you doing something wrong? The reservoir should not be totally full!)
Do you have any idea how quick engine damage happens when the engine gets overheated?
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Is the oil level going UP? If it is gaining on the dipstick, then the coolant is going into the crankcase. Will look like a chocolate milkshake.
Internal crack in the area of the oil separator baffle on the back of the block is the suspect area for one of the possible block cracks. You can't see it without some disassembly.
The external block leak would be on the front of the engine, you should be able to see it if you look. Found this on a GIS, the circled areas are where coolant can leak from:
Either of these leaks are covered under the 8 year unlimited mileage warranty extension. All damaged parts from overheating are covered as well, as long as the block is at fault.
If something else like your water pump or a hose has been leaking, that's technically not covered by the block warranty extension.
See your dealer. It is up to them to make the determination.
Have ALL recalls been done? There were belt and tensioner and pump pulley related recalls. See your dealer.
Recently worked on a friend's '06 Civic, north of 200k miles. Coolant was found to be mixing with the oil, it was overheating from the coolant loss. Originally suspected a possible failed head gasket as that's usually the cause. Found the TSB for the cracked blocks here. Did not realize one of the possible crack locations was behind the air/oil separator cover which would cause coolant in the oil.
Back of engine with the oil/air separator cover removed. Clear signs of coolant and a small crack in the block. Owner tried putting in head gasket leak fix, you can see it gummed up. Small crack visible above the red line. This was the best picture I could get with the engine still installed.