Temp range (-40C to 150C) is a big constraint but does it mean that ARM can't live upto that?
150C is quite high and limits your options. A range of -40C +105/125C is more normal for general automotive stuff.
If you intend on mounting the device in the engine bay, either hard up against the engine or bolted to it, then yeah, you will need some pretty high temp mcu.
I would avoid mounting stuff near the engine for that reason..
I don't think they're are any laws regarding what mcu specs you "must" use. It's up to you what temp range you decide is necessary or your application.
You do need to keep in mind the rules if you choose to get your product certified to one of the automotive standards so you can display the compliance on the product.
For example, your product maybe fine with a normal -40C +85C mcu but the certification may say that all mcus have to be -40C +125C no exceptions.