Hello there,
normally you have ½ -degree angle for all wet capstan on so-called tandem drawing machines. The dry capstan or rather pull-out-capstan doesn't have any angle and is straight cylindrical.
Lately you also find so-called bi-conical capstan for rod break down machines. The purpose here is that you can turn them around after you get wear grooves. They have a ½-degree angle, too.
The angle has to do with the slip and the wire alignment inside your wet drawing machine. It prevents wire crossovers, what very important on today’s multi-wire machines.
The taper on the capstan has nothing to do with wire temperature.