I have stage 4 copd and in the hospital . my body temp has dropped from 97.6 to 96.2 is that normal even with an infection?

Possibly.: Low temperatures are sometimes indicative of infection just like high temperatures. That temperature is not one to worry about though, it likely is just normal fluctuation and will improve. In general doctors are wise to be vigilant for infection when seeing low temperatures, although yours is not that low so I wouldn't worry too much about it.