I've been a competitive Adventure Racer and Ultra-Runner for the past 15 years, and have spent a lot of time traveling at night. The most important part of making it safe and enjoyable, is good lighting. I find that small, LED headlamps are either not strong enough, or cast shadows on the ground which make it hard to see. Make sure to get a light that you can switch to Halogen, or can increase the lumens on. This is necessary when you are route finding, or need to get a bearing on your surroundings. I've also seen people use Red or Blue lights at night, which helps you to see variation in the terrain better. Some people like wearing a light around their waist, others on their head, and some like to just carry a hand light (or a combination of all three). You will have to experiment to see what works best for you. I like to wear a headlamp, but after many hours, the weight of the battery pack can give you a headache. I alternate with a lightweight Surefire hand light. Expect to spend a bit of coin in this department.
I rarely get cold at night, as long as I keep moving. Don't stop for too long if you can help it, and always pack warm clothing. A wind jacket, rain jacket, hat and gloves should be part of your basic kit. Layering is key.
A good trick to combat sleepiness, is packing chocolate covered espresso beans, or small 5 hour energy shots. Just keep in mind that caffeine is a diuretic, so don't forget to stay hydrated (even if you're cold and/or not thirsty). Some people get a bad case of "Sleep Monsters" when going for long periods of time, others don't. It just depends on the person. If you've been going for over 40 hours, it's proven to be more efficient to take a quick 10-15 min nap. You will wake up refreshed, and re-energized. Most people do not need to sleep when running overnight.
I've rarely encountered wildlife at night, but don't be surprised to see eyes reflected back at you in the bushes. Mostly you'll just see bugs.
Running at night is magical. It's a whole different world that few people have the opportunity to experience. Enjoy it!