2013 Prius Three - shaking at startup, but not every time

Good afternoon. I have a 2013 Prius Three I purchased used in October, 2016. It had 91,646 miles when I purchased it, and it's now approaching 125,000 miles. I have full maintenance records from pre-purchase via the CarFax report, and it was maintained at the dealership approximately every 5,000 miles.

I've noticed on a few occasions this winter that the engine will shudder and vibrate rather dramatically at start-up. It did this once when I came out after work on a cold day. I shut it off and back on, and it ran normally after that. It did the same thing a few weeks later when starting it up at home. Again, turning it off and on resolved the issue.

I have noticed since these happened that the engine seems to vibrate or shudder for just a moment when it shuts off at a stop. It almost makes me think one of the engine mounts has gone bad, but it seems very intermittent, when a broken mount would be a problem constantly. I do not have any dash lights or codes. As far as I am able to tell, it is not leaking or consuming oil.

When I took it to the dealership for the recall at the end of January, the service tech mentioned that I should get the spark plugs replaced soon, as they can "cause trouble" if they aren't replaced. He didn't elaborate on what that meant.

Seeing the threads about head gasket problems has made me very nervous, but my symptoms don't match exactly. My vehicle was built after the redesigned intake manifold was rolled out. Does anyone have suggestions as to what I should be looking out for, or maintenance I should be doing? I appreciate your time.

 

Thanks. I’ll check out the EGR.

The coolant level is good. The dealership changed the engine and inverter coolant before I bought the car at 91,000 miles. That does remind me, though — when it was warmer, I did notice the coolant would hiss after the vehicle was parked and turned off, and there are some small spots of dried coolant on top of the reservoir closest to the right fender. I’m not sure if that’s related in any way or anything to worry about.

 

Unfortunately, my Prius was totaled in July by a girl in a Mercedes looking down at her phone, so I never got to the root of this issue. A flight of angels sing thee to thy rest...