What happens if you touch a bioluminescent animal?

Nothing. Bioluminescent animals are also made of meat like we are, if they release too much heat, they would cook themselves. Most bioluminescence are from the breakdown of luciferin by a luciferase and the reaction tends to be very efficient, so very little waste heat is produced. We very commonly use bioluminescence for experiments, I have personally done a lot of experiments with genetically modified flies that would produce bioluminescence upon feeding of luciferin