Don't start it cold...
The temperature of your meat BEFORE you start cooking is very important. You want to keep the meat safe and chilled below 40F before you cook it, but you need to give it time to warm up (un-cool really) a bit before it goes into the fire.
Most bacteria that turns meat bad starts out on the surface, so if you plan on using a salty rub or a simpler salt-based seasoning, apply it while the meat is coming to temperature.
If the temperature in the room is really hot (more than 80F)
you might want to find a cooler spot or a different technique. When the internal temp is 55-60F you are ready to cook. The advantage of doing this is that the meat will cook quicker and more evenly.
By getting the core of the meat to desired temperature sooner, you won't need to cook the outside longer than necessary, you will retain more juices and have a better tasting result.