I used to clock in long sessions at the gym right after my night
shift, 'Because I can!' (sorry, Bear... just infringed on your
copyright! hehehe! 
) and because it helps me to sleep soundly for a few
hours straight if I tire myself out with exercises.
That is, until colleagues warned me that exercising when your body
is exhausted, ie. after night duty, can do more harm than good. And
then, a friend told me that a nurse did that very routine, and
fainted and collapsed, and ended up in the A&E!!! 
So, don't go overboard and don't over-estimate your own fitness
level! 
BTW, half an hour at what speed? If you're doing high-intensity
varied 'interval training', then yes! If you're going to exercise
for half an hour at a pace where you can still talk without getting
winded, then maybe you ought to kick it up a notch.
A lot of interesting things to learn re exercise. Hey, get 'Shape' magazine every month, the local version!
They have a lot of interesting articles on exercising in there!
