How hot is a pot of simmering water?

At the interface between the liquid and the steam, where a bubble is coming to the surface, it's at the theoretical boiling point. At the surface, the water is evaporating rapidly, with the substantial heat loss that entails. In between, the water is at intermediate temperatures.

From practical experience, food that's just simmering will cook much more slowly than food that's at a full boil. But quantitatively, how far below the boiling point is the average temperature in a normal-sized (say four liters) pot, when it's being heated with a normal stover burner, just enough to produce observable bubbles of steam at one or two places where the burner provides the most heat?

Edit: The characteristics of the pan should make a difference. A large flat pan provides more of area for cooling. What I'm interested in is the range of temperatures that could exist under realistic conditions.

So to make it specific, let's assume that we're looking at two pots, one that lets the water be cooler and another that keeps it closer to full boiling temperature. In the first case, the water is 8 cm deep, so that the pot is 2*sqrt(4000 / 8*pi) = ~25.2 cm in diameter. The edge of the pot extends one cm above water level. The pot is steel, 1mm thick, and sits on a burner 20 cm in diameter, contacting it at three points each 1mm square, evenly spaced around the edge of the burner, and there's a clearance of 0.5 mm everywhere else. Burner and pot-exterior both have albedo of 25%, and the whole burner is at uniform temperature, just hot enough to barely make the pot simmer. The air is 20° C, 1 atm pressure, the humidity is 30% (corresponding to a dew point of about 6° C), and there's a breeze of 1 meter per second.

In the second scenario, concocted to keep the water temperature as close to the boiling point as possible while still counting as "simmer", the water is 10 cm deep, so the pot is 2*sqrt(4000 / 10*pi) = ~22.6 cm in diameter. The bottom of the pot is perfectly conductive, so that the entire bottom surface is at a temperature of exactly 100° C (or infinitesimally above, as water gets ever-so-slightly superheated between bubble nucleation events), and bubbles form wherever nucleation happens. The pot has a lid, which allows steam to escape as it's produced. The lid and the sides of the pot are steel, 1 mm thick, and the air in the room is at 25° C. (Because of the lid, the humidity is irrelevant: inside the pot, there's just steam at 100° C.) Enough heat is added to produce 1 cc of steam per second in addition to whatever condenses on the lid, rattling the lid just a little so that you know it's simmering.

Or pick any set of conditions you have a source for, if you have one.

Edit again: A crude measurement with a meat thermometer looks like about 205. Wikipedia mentions estimates of 180 and 200, but their sources don't look all that solid this time.