I'd guess a 2.2kw spindle will produce far less than 500W heat, as electic motors are 90%+ efficient, and the bearing friction won't contribute that much to heat.
Personally, I'd opt for a copper coil. Get a coil of 8 or 10mm copper pipe, make some holders to space and secure it (basically some bits of MDF/Plywood notched out to accept the pipe) and pipe it up. You'll still need some kind of tank to allow for expansion though.

I certainly wouldn't be using a car radiator, as they're designed to deal with 10's of KW of heat. A heater matrix would be more suitable, but it's quite hard to get them with basic pipe connections, and it's not worth scrapyards removing them as they take that long to get into.