1981 320i Starting problems

[rollernose]

I just bought an 81 320i that needs some work. It starts fine cold but idles a little rough and at a high rpm. After it warms up you can shut it off and start it right back up. But if you let it cool off a little it wont start until its completely cold again. It will crank and light up for a second or two but dies every time. ??? Any Ideas, I'm 18 with a tight budget but this is a cool car and I would like to fix it up and drive it to college!

Thanks