Yes, it's possible that Bikram Yoga can cause heat rash, usually in people who are new to the practice. It's not common but I know of a few instances.
First I must emphasize that I am NOT a doctor nor am I qualified to give medical advice. What follows is from my experience as a yoga instructor and is only my personal opinion.
Heat rash is caused by blockages in the sweat glands. The exact cause is unknown but high heat and humidity can be contributing factors as can any activity which results in intense, heavy perspiration. It usually occurs in parts of the body that are covered by clothing.
Some contributing factors to look for are: clothing that doesn't allow your skin to breathe (cotton is not good in class -- it's best to wear workout clothes that allow wicking), bacteria and heavy or greasy skin creams. There are also medications that have been linked to heat rash.
Heat rash should go away on it's own in a few days -- providing you avoid high heat and humidity -- so it's a good idea to take a break from your practice to see if the rash will clear up on it's own. If it persists much longer than that or if it gets severe (swelling, pus, fever, or swollen lymph nodes) then you should see a doctor.
One student, who also happens to be an MD, told me that he found a vigorous scrubbing of the area with a a dry brush to be helpful in speeding up the healing process.
