More than likely it is your heater core that is leaking. What happens is when your thermostat opens, it sends the warm water to the heater core and causes a rush of steam. And no offense, but if you aren't even sure that it is the heater core, it's going to be a tough job....I just changed my heater core in my '86 Cherokee this past sunday. What i thought to be a rather minor project took me all day to do.
The plastic box that encases the blower motor, the a/c condensor, and the heater core is located under the passenger side of the dash, and I do mean UNDER the dash! It goes from about the ashtray all the way to the passenger side door. There are five bolts that hold this unit in place which are located in the engine compartment on the firewall.(A few of them are in real dandy spots) All of the bolts have to be removed and the entire unit has to be taken out. It is by no means a fun or easy task...If perchance I ever have to change it again, I am selling the damn thing!!! If you do decide to tackle this project and you have any further questions, feel free to give me a yell and I will help out in any way I can.