Prepping for cold weather tri

I just signed up for my first triathelon to be held the end of April in northern South Dakota. While the weather could be wonderful, there is a high potential that temps will be near freezing. The tri starts with a pool swim that does not allow wet suits. It then has a timed T1. This race is notorious for sending droves to the ER with hyperthermia. How do I handle this transition while making sure that I stay safe on the bike ride?