So steam is caused when you have a supersaturated water vapor that cools and forms large suspended water droplets in the air. This is governed by the kelvin equation which you can read more about here:
To get larger water droplets, or in your case a denser looking steam, you have two options: 1. you increase your partial vapor pressure or 2. you decrease the temperature. Without knowing more details, my guess would be your flame was also supplying a substantial amount of heat to the air around the water vapor. When you turned the heat off, the air cooled much more rapidly than the water and caused the vapor to condense more rapidly.
One easy way to think about this is breathing in the winter. When you blow hot moist air out of your mouth, you see steam. When you are in a warm building, you don't.