This question gets asked all the time. The answer: although training in the heat will help you acclimate to a hot race, it will not improve your fitness or race times in milder temperatures.
There are MANY things, aside from heat or humidity, which can make a run more onerous -- running with a backpack, with ankle weights, or while juggling. If you become accustomed to such a burden, subtracting it will always make running seem easier. However, very few extraneous burdens actually yield a training benefit -- i.e., faster race times than would have been obtained without ever undertaking the burden. Altitude and hills are two notable exceptions.
If you understand the physiological effects of heat, then you will appreciate why it does not help training. The body responds to heat by diverting blood to the skin. Increased blood flow to the skin for cooling results in less blood flow through the muscles, and taxes the heart. Note that a reduction of blood to the muscles lowers the ceiling on the work they can perform, thereby limiting training. When running in the heat is prolonged, dehydration through sweat reduces the blood supply and also increases blood thickness, further taxing the heart. The net result of hot weather training: because the cardiovascular system plays a central role in cooling the body, at any given level of cardiovascular intensity, the muscles can do less work in the heat. This is not a formula for successful training.