Does the body burn more calories when you have pleurisy?

Yes. The body may burn more calories during any acute or chronic inflammatory process in the body. With pleurisy the underlying cause may have a significant impact on your metabolic rate & hence the total calories burned. There is not a lot of scientific literature that exactly quantifies how many extra calories are burned in pts with pleurisy, but you should discuss it with your doctor to adjust diet.
Inflammation. I guess, but not incredibly faster compared to not having pleurisy...