What could be the problem in a 1993 corsica that runs hot after you have changed the thermostat - is fine in the morning but as the day gets hot it runs hot and steams?

You may have not enough coolant or the wrong kind of coolant. You may have used a winter thermostat rather than a summer thermostat. The radiator cap may not be the right one or isn't functioning properly. The pressure escape line off the radiator may be obstructed. Your radiator may have a number of fins clogged, or the coolant pump may not be operating properly. The fan belt powering the pump may be loose or slipping. There are multiple possibilities!