Trouble starting

I have a '91 Plymouth Acclaim; Mileage: 145,422. Just recently, my car has had trouble starting. When starting the car in the morning, it will start, but after a few minutes it will cut out. I've noticed that when restarting it a couple more times, the car runs smoothly only when the temperature guage moves to hot and then levels out. However, if it has been more than five hours since I last used the car, it will do the same thing until the temperature gauge heats up. My car has been overdue for an oil change, as well as fuel filter change. Could that be the problem?