[Chickensoup]

That is my question. How do I turn that capability off. How would they do it? Would the car be broadcasting?

[Myrddin]

The cars with WiFi typically have a very weak transceiver. Just enough to work inside the car. They need an external carrier e.g. 4g LTE or similar offering to be internet connected --or-- a Bluetooth sharing of the connection to your own phone.

You'll have to start with contacts at your car dealer to see what can or can't be turned off. If you have a Linux PC, you can hookup to your WLAN and start with an "nmap" scan against the default route offered by the router. You can also get a copy of "nessus" to have a quick look. Securing the WLAN with WPA2 encryption with a long, complex password coupled with turning off SSID broadcast will help hide the presence of the WiFi in the car. Adding a MAC filter to only allow specific devices to connect is useful too. That's the first line defense. Turning off unnecessary services exposed by nmap/nessus also reduces your attack surface.