1998 Acura Integra Now the car starts and runs well until it gets hot

My Integra has been with me for many miles since I bought it new in '98. The car has been great! I am having a problem now however, which started about 10,000 miles ago with a leak in a radiator hose which caused the car to overheat a few times (I kept re-filling coolant when it overheated) until I realized it was a hose and got it replaced. Now the car starts and runs well until it gets hot. Then it starts to sputter and idle very rough, it also seems like I am getting gray smoke (only after driving for a while) from the exhaust. Again, when the car is cold it runs very well for about half an hour then it starts with the sputtering and smoke. What do you think is causing this?