My ‘13 prius v 5 with tech package with 67k miles recently began rattling and shaking when the ice started cold. On a road trip last week, I drove it hard on interstate entrance ramps. I’d go from slow to 75mph at full throttle. I did this several times. This week, the ice has started as smooth as brand new upon cold start. Perhaps it just needed blown out.
Pull the airbox and throttle body off of it. Check to see how much PCV crud is laying down below the throttle body. It’s more prone to being sucked thru the intake into the engine at cold starts. Clean it all up and install an oil catch can between the intake and throttle body.
probably just the normal gen 3 cold soak problem. you can find several threads here, and thousands of complaints.
Toyota has acknowledged "rough idle at cold start", and is pointing the finger at carbon build-up in the Exhaust Gas Recirculation (EGR) system. This is a Canadian Warranty Enhancement Program notification I got, in May of 2017. In the header is "SOSH-W11-1A". Was there a similar notice in the States.? This notice is for our Canadian 2010 Prius, fwiw. The trouble code in the above is P0401 (it's getting cut-off in my pic). BTW, regardless of the above notice, my 2 cents: if you're at all mechanically competent, I think DIY is the way to go for this. If you've got the time and patience you can restore your existing EGR system to as-new, for little or no expense.
I had this on my 2013 with around 100k miles. I cleaned the intake, changed the pcv, and it hasn't done it for the last 20k miles. iPhone ?