If I may, I'd like to reframe your question in the following way: "Is rigorous physical exertion in a room heated to 83º safe for a person with asthma?" And that is best posed to one's healthcare practitioner of choice.
As a yoga teacher of ten years with therapeutic and restorative training, 2000-hour certification from the State of Washington I would not likely recommend such a thing for my students with asthma.
That having been said, it may be perfectly fine FOR YOU to take such a class. Different bodies are affected in different ways from different things. And there may be some benefit. But from where I sit the potential detriment far outweighs the potential benefit and it's simply not a safe path.
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