The temperature will determine colour. 5000-6000k will be a nice white colour I guess. The higher you go the more blue it will get. My HIDs are 8000k and have a good aqua blue tint to them which doesn't match the xenon headlight but looks better than the stock angel eyes did when combined with the headlight.
HID definitely gets hot - if I'm in very slow moving traffic for a prolonged time I feel like I can smell the heat when I open the window (or perhaps I've become paranoid) but yes you can definitely feel the heat when you put your hand to the headlight covers under the hood.
But I've run them for a good 3 hours on highway driving, pulled over and checked the temp and they were cool. So I've tended to turn off the daytime running lights when buzzing around town during the day, but they hold up fine on high speed driving.