DC Running Coach is operated by Mike Hamberger, whose career as an endurance athlete gained many accolades, including All-American honors in triathlon and a marathon PR of 2:46:33. Mike was a track & field coach and faculty at Sidwell Friends, and now teaches undergraduate sport psychology. Mike offers custom training programs and technical instruction in running mechanics for athletes of all abilities. Buy Mike's book, "The Art of Run Training": http://amzn.to/1EDI6uB
First, racing in the heat is tough, especially the longer distances. There aren't many summer marathons scheduled in hot regions for this reason. Some race directors are quite honest about discouraging beginners from entering their marathon because of the safety concerns. During the summer, I recommend short-distance racing for the runners I coach. Fortunately there are twilight races in the DC area. Check the calendars.
I rarely cancel the group track workouts I coach because there are many ways to get around having to scratch the workout completely or moving it indoors to a treadmill. Everyone should obviously know their limits, and not everyone is affected the same way by the weather. When considering a tempo workout on the track, the general alterations to your workout are to, a) slow the pace ~10 - 15 seconds per mile, b) take an extra 20 - 30 seconds between reps, c) cut the distance of the reps 200 - 400 meters, and d) reduce the number of reps you are running. In some instances, you can take all four precautions. The idea is to keep getting exposure to the elements without overheating yourself and/or getting too far out of the training (heart rate) zone.
We all know the importance of hydrating and we all see the popularity of water bottle systems, like Fuelbelt, being used on distance runs, but I am surprised at how few runners hydrate during track workouts. Your heart rate is obviously higher here than on your distance run, so why not take extra steps to keep the heart rate down? You need to keep water in the muscles to keep them functioning optimally. Being hydrated has less to do with whether or not you have cotton mouth than it does the state of your muscles, specifically, preventing premature fatigue. There's a thin line between being tough and being foolish. The goal of every track workout is quality reps. The instant you become dehydrated on the track, you're engaging in low quality training. In other words, in order to race fast, you have to train fast. Take a water bottle with you and hydrate between reps to keep the heart rate down and to have a high-quality workout.
As far as going shirtless (for the guys) or wearing a sports bra, it can be an individual preference. The benefit, even compared to wearing a lightweight singlet, is that less skin coverage is better in terms of sweat evaporation and cooling the body. However, if it's a relatively long run/race on a bright, sunny day, the direct rays against your skin will add to your core body temperature, so experiment and choose wisely. If you anticipate racing in hot/humid conditions it's a good idea to do a training run in the exact clothes in which you're going to race (hat/visor included, if applicable). Then you'll know if your race clothes are comfortable enough. There should be no surprises on race day.
Also consider whether or not you have the capacity to change your race goals in drastic weather. Some athletes are not wise enough to do this, so they end up feeling like the day was unsuccessful because they only focused on the finish time or certain splits instead of keeping things in perspective and having multiple goals (e.g.,process goals).
Finally, embrace the opportunity to run on a rainy days (not a thunderstorm, just rain). The rain will keep you cool. I will admit there is a bit of toughness that develops from training in the elements, but it does not (and should not) have to be a constant. Knowing that running in the humidity each week can be difficult, running in the rain does make some sense. Plus, it could rain on race day and you'll know ahead of time how you handle it. Don't let it ruin your plans. If it's raining, then see it as a chance for a PR—most running records are set on overcast days with temperatures in the 50-60s.