Not close enough to the Sun
The Roadster's orbit has a perihelion (closest distance to the Sun) of 0.98 AU, that is to say only very slightly closer than Earth orbit.
From Elon Musk's Twitter:
At Earth Orbit, the influx of energy from the Sun is about 1300 Watts per square meter. This is not far from the maximum we can have on the Earth surface. The atmosphere does dampen a bit, but at most we can get 1000 W per square meter at the equator when the Sun is at zenith.
The temperature of an object depends the flow of heat to it, and the flow of heat from it. If there is more heat coming in than is going out, the object heats up. When more heat is going out than is coming in, the object cools down. When these things are in balance, the temperature is stable.
On Earth, there are (chiefly) two things that brings heat to an object: the convection/conduction of the atmosphere, and radiation from the Sun. The atmosphere is a huge contributor there, at a balmy 300+ K in regions where we would even begin to consider melting plastics on an automobile. So the "baseline temperature" of an object in the Earth's atmosphere is 300 K.
Add to that another 1000 Watts per square meter from the Sun and you can have so much energy going into an object that it heats up and can eventually achieve temperatures that can melt plastic in/on a car. This is especially so if it is a coupé car, that traps warm atmosphere inside.
But in space, you do not have that atmosphere, and this was not a coupé but an open top car. Hence the baseline temperature of the car when in space is not 300+ K but 0 K.
Note the distinct lack of an airtight enclosure around any plastic details
So while the second contributing factor — solar radiation — is indeed 30% higher in space than it is on Earth, the lack of the first one — a warming atmosphere — completely negates that. The car will most likely freeze over time.
As for degradation: yes, that will happen over time. But not so much due to temperature as to ionising radiation. We are fortunate here on Earth to be living under a protective blanket that is the atmosphere that keeps away most of such nastiness. In space... no such luck. As the Roadster coasted around in the Van Allen belts for a few hours before being sent off for good, some people reported already seeing radiation damage on the windscreen, I assume some "yellowing" of the plastic laminate.