I would definitely strongly advise you NOT to cycle to work. I find that if I ride gently...I get cold, thus not helping my cold in any way, and if I ride fast, I get hot and exhausted...also not good if you're ill. Your body temperature is bound to increase, even with just a light form of exercise, and will then rapidly decrease once you're off your
bike and inside at work. It's a lose-lose situation whether you go fast or slow, so just take the train. I ignored my own advice and am now paying for it...my cold is taking ages to go away!