Well, how frequently do you work out? If you're typically sedentary or are in poor cardiovascular shape, the lungs can feel a burning sensation. This is a result of no exercise adaptations in muscle cells. Untrained individuals have more fast glycolytic muscle fibers (compared to fast oxidative glycolytic fibers), which use carbohydrates as their fuel. The carbohydrates create more CO2 per O2 consumed. The lungs can't diffuse the CO2 out of the blood quickly enough, resulting in a pH increase in the lungs (thus the burning). Work out more frequently at lower intensities. As you train your body to the type of stimulus you want to do, it will adapt.
Also, it COULD be the way you breathe. In the nose, you have little conchae (bony shelves with mucosa around them) that increase surface area. That increased surface area allows for greater humidification of the incoming air. If you breathe through your mouth, you're allowing dryer air to get into the lungs. The dry air may be irritating your bronchi. When you're working hard though, it's hard to breathe in and out of your nose. My bet's more on the first explanation.