Most of your training will be outdoors, as it should be. With rare exceptions, your triathlon will be outside. That means that, on occasion, weather will be a major factor in your workout.
The most threatening will be hot weather. You don't want to avoid warm-weather training altogether because you will almost certainly need to become acclimated to the heat for your race. Common sense is in order, however.
You have already been told to stock up with light-colored, loose-fitting apparel for your training. Now wear it.
If you live in a warm climate, avoid training in the middle of the day, when the sun is high in the sky and temperatures are at their worst. Get out of bed early or wait until the sun is down or going down and conditions are more favorable.
Always take lots of fluids and have them at hand when you are running in hot weather. Dehydration can be a very serious problem. If you can, train with at least one or two other runners so that assistance will be at hand if you get into trouble.
It's okay to brave the elements for a training run in the heat, but don't let bravado put you in danger. If it's just plain baking outside — temperatures in the nineties or a heat index approaching triple digits — do your run on a treadmill at the health club or at home, or just let it go for the day.
Rain is a separate issue. Except in cold weather, rain can be refreshing as it cools you off while you exert yourself. Face it, if you have a workout of more than fifteen or twenty minutes, you will probably be soaking wet from perspiration anyway. The main caution about rainy weather is lightning. If lightning is present, go home. Plan to run another day.
When running at night, always wear gear with reflective strips, and avoid running in the dark on streets or roads with heavy traffic. No matter how easy it is to see you, drivers who aren't paying attention won't notice, and you know there are plenty of them driving the streets. Stay away from traffic. Even if you aren't struck by a car, you will still be breathing fumes that can irritate your airways.
Running in cold weather can be invigorating, and it doesn't sap you like the heat and humidity. But there are dangers in extreme cold, and you should always wear layers and a head cover when temperatures are freezing or lower.
If wind chill is a factor, make your outer shell a windbreaker, and always wear gloves. Remember, too, that cold weather doesn't mean you don't perspire. You don't notice because it's not pouring off of you as it does in the heat. You are still losing fluid, however, and it's just as important to stay hydrated when you are running in the cold. It will take you longer to warm up in cold weather, so add a bit of extra time in slow mode before you start pushing hard in your run.
A key advantage to treadmill training is that once you set the speed, you have to keep up or you will go flying off the end. It's a good way to do a tempo run, the goal of which is to sustain a speed for a set length of time.