The weak point is probably going to be your car's accessory (cigar lighter) port. They can handle 120-150W, but if the contacts are corroded on either the socket or your plug that number goes down and the connector heats up.
I charged my battery in the car last winter with a 36V2A charger. That's about 80W max. I had a 500W inverter. It handled it fine, but the connector did get fairly warm. I've had that inverter for many years The label says to not go over 150W with an accessory plug. I would have to connect it direct to battery to get 500W out of it.
.