Entropy and Open Systems - AP Biology
You are correct. Anything within the universe is part of the closed system of the universe. Therefore, they must also increase the entropy of the universe. You are correct, they do release a lot of heat. Plus, while making ATP, the major source of cellular energy, they convert a complex molecule, glucose, to simpler molecules, H2O and CO2, increasing entropy as they release these chemicals. 

Also, the key fact is that to lower entropy in their body, organisms must use up energy. Energy is required to avoid the entropy from increasing (which actually means they actually expend energy to prevent equilibrium; high entropy means reaching equilibrium). So they would follow the 2nd law of thermodynamics. Which reminds me of a joke!

Old chenists never die, they just reach equilibrium!