Exercising in the heat brings with it several important considerations.
One area of concern is a dangerous increase in core body temperature. The human body is designed to cool itself by evaporation of sweat.
Changing a liquid to a gas requires energy; as the water portion of sweat evaporates, it removes heat from the body generated during exercise which allows the core temperature to stay fairly stable. Most of the time evaporation is a very efficient cooling mechanism. This changes when high temperatures combine with high amounts of humidity. Relative humidity (RH) is a measure of the nearness of air to the saturation point where 100% RH means the air is completely saturated.
Every air temperature has a particular amount of water vapor that can be evaporated into it. When levels of RH approach 100% there is not much space available for additional water to be evaporated into the air. The combination of warm temperatures (where evaporational cooling is needed) with high RH (where evaporation will not happen as easily) can lead to the body being unable to cool itself efficiently, resulting in the core body temperature increasing. This temperature increase can lead to heat exhaustion and heat stroke, the latter of which can be fatal. The heat index temperature takes into account the level of relative humidity along with the actual air temperature to determine how warm it actually feels to the body as a result of less efficient cooling. When thinking about exercising on a hot and humid day (usually temperatures greater than 80*F with a RH=45%), make sure to take a look at the heat index (heat index calculator: http://www.hpc.ncep.noaa.gov/html/heatindex.shtml) to see how warm it will actually feel when you are outside. In some cases, you may need to shorten your planned workout or find an air conditioned location in which to exercise.
Another concern when exercising in the heat is dehydration. Warm conditions will make body temperature climb more quickly which in turn increases the production of sweat. If the liquid that is lost through sweat is not replaced, dehydration can become an issue. Severe dehydration can lead to shock which can be a life or death situation. (http://www.webmd.com/hw-popup/shock-in-adults-and-older-children).