This is a helpful article…
This is a helpful article with a lot of comments that I stopped reading after the first page, so I do not know if anybody has previously suggested the following simple workaround/troubleshooting method. My 2011 Prius developed this issue at around 205,000 miles: it would run rough when starting but after a couple of seconds would be fine. It was showing misfire codes. After learning about the head gasket problem and the rough startup being due to coolant being forced into the cylinder through a leaking head gasket, I figured this was only a problem when the cooling system was pressurized after driving. The coolant recovery tank is pressurized, so I started loosening the cap after driving to depressurize it. As long as the engine is not overheated, there is no danger of scalding because the tank is not full to the cap. I leave the cap loose until the next trip and loosen it after every trip. I also put a cheap $3.00 ELM327 code reader on the OBDII port so I can read the coolant temperature on my phone and it has never overheated after 6,000 miles of driving and always starts and runs find and is throwing no codes. So not only is this a workaround that works indefinitely as long as you do not mind the hassle of loosening and tightening the coolant recovery tank cap, but there is no doubt that my engine is fine and is not overheating, so it would be worth replacing the head gasket. That said, I only use the car locally and I would definitely replace the head gasket before making a long trip and I plan to anyway when I get the time.