My 1.83 Ghz Core Duo MBP gets warm, but the only time it gets hot is when I'm doing something that's processor intensive. Right now I'm running Safari, Mail, iCal, iTunes, NetNewsWire, Preview, and Keynote and it's just a little warm. I've been browsing and putting together Keynote presentations for about an hour or so.
I would recommend checking the battery to make sure it's been replaced and definitely max out the ram at 2 gigs if you're running Leopard. I've had mine for two years now and I'll be running her until this time next year when AppleCare runs out. Just make sure you check the machine out and make sure that everything is in good order.