How close can a battery be next to an engine?
If its very close (less than 10mm) what problems would it cause?

I depends on which bit of the engine!!

n/s engine cover. gets hot!

Heat is bad for batteries.

Could you fit a smaller battery and a heat shield of some kind?

The battery in my TT is about 8" from the cylinder head and boost pipes run underneath it.. needless to say it gets too hot to comfortably touch..... presumably the Audi Engineers knew what they were doing when they put it there ?!?

interesting, ok thanks guys. Think Il move it away as much as I can and fit a heat shield.
Recommendations on shields? homemade/bought