Electrical, automation or mechanical technology are also good ins for factories. Except in that case you're not building cars, you're maintaining the machines that build the cars.
And contrary to the average expectations, you'll make a crap-ton of money in industry. It's far better than consulting engineering and I kick myself for going into that instead of taking the Dofasco job that was offered me.
The industrial career path is as follows:
1) work at a consultant for 2 years for shit money, just til you've learned the basics and get to meet a vendor.
2) quit your consulting job, go work at a vendor. They give you super-specialized training in the equipment they build to solve difficult problems in automation. The one-week training courses they offer to outsiders are nothing compared to the stuff you learn as an insider.
3) after 5 years, quit the vendor and go work for a factory, implementing the solutions you learned at your vendor.
4) if for any reason you get tired of working at that factory, go to another vendor and repeat the invaluable training experience with another product line.
5) Eventually you can go back to consulting, except this time as an automation specialist who can literally write 6 random numbers on a piece of paper, hand that paper to his boss, and tell him you're getting paid that many dollars this year if the office wants to stay in business, bitch.
Alternately, you can just stay at the factory's engineering office, and learn the super-expensive program they use to design axles or whatever. I knew a guy who had his own Sun Sparcstation AND another minivax at his desk, one to run GM's $100,000 program and the other for Ford's $100,000 program. That guy was set for life.