I'm not sure if mythtv is available on live cd. Even if it is you're gonna have to reskin it for car applications so unless you wanna redo it everytime you boot off your live cd you're better off installing myth and skinning it and then having linux boot load up your window manager then right into your carpc version of mythtv.
You might want to check out knoppmyth, it's a debian based mythtv install. the basic window manager is fluxbox and it boots right into the mythtv frontend. The nice thing about it is that it is super easy to set up. I've installed it on a PVR box I use at home. Works flawlessly and it was a 45 min install from start to finish. (that's also provided you're familiar with the debian package manager) IMO it's not as good as portage(gentoo). but it's still pretty easy.
Anyhow hope that kind of points you in the right direction,