What temperatures correspond to the settings on a stove knob?
As ferret said, you cannot associate temperature with a burner. All you can do is adjust the heat output. (ie BTU, joules, watts or whatever you measure it in.)
The big problem for most gas ranges is that the amount of heat produced by most burners does not increase uniformly, but will suddenly increase as you rotate the knob.
In an ideal world it would be approximate a logarithmic setting. For example, suppose the control know had 10 positions, and the maximum BTU was 12,800 at position 10 and nothing at position 0. This ideal control would chuck out BTUs something like this
10 = 12,800
9 = 9000
8 = 6400
7 = 4500
6 = 3200
5 = 2250
4 = 1600
3 = 1150
2 = 800
0 = off
However, I am yet to see a control that comes anywhere close to being uniformly smooth through its range.
Paulustrious: In fact, it would be possible -- but I do not know whether any maker implements the theory -- to make an induction burner that would control by specific temperatures.
Every induction burner of which I am aware contains an integral thermometer for two functions: (1) to shut off the unit before the circuitry of the inverter unit overheats, and (2) to activate an indicator light to show which burners have recently been used and the Ceran top there has been made hot by the pot that was resting upon it. The latter function will also be activated if a hot pot is removed from one burner and placed atop a cold/off burner.
Now, those two functions can be achieved with fairly simple binary single-temperature-point thermostats, but there is no reason why more sophisticated thermostats could not be integrated with the control settings of the burners.
But what temperature are you trying to measure? The water in a pan? The metal of a pan without anything in it? The flame? The heating element?
My inexpensive table top induction burner has 'temperature' settings, but they really are like the power settings of a microwave. The induction coil just cycles on and off. Yes, it can detect whether a coil is on, and whether there is a pot of the right size on it, but it does not actually sense the temperature of of the food or pot. That would require a probe that is placed in the food.
What does the glass top stove manual say about the settings?
In an electrical system anything is possible - for example, a standard electrical probe that feeds back to the cooker. If the burner induces electrical currents in the pan then they could be detected - although I do not see a simple way to relate that to temperature. An alternative is the old-fashioned 'don't-boill-the-milk' sensor that could be embedded in the middle of a burner. I had one of those in a cooker that dated back to the early seventies. Other options could be a strain gauge embedded in the cooktop, a temperature transmitter similar to the ones used for heart rate monitoring, 'intelligent' pans that picked up energy and transmit their temperature, radiation sensor embedded in the cooktop and so on. Sooner or later some feedback method will be incorporated in induction tops.
It would make it easier to cook silas mariniere.
On a gas stove, the temperature of the flame will be about the same regardless of the setting. I'm less sure about the electric. But what varies is the amount of heat produced, not the temperature.
A pot of boiling water will have the same temperature regardless of the burner setting - until the water boils away.
Electric ovens have a thermostat that measures the temperature. When hot enough, it turns the heating element off, and then back on after things cool a bit.
There's no temperature/setting association possible on a cooktop. That's limited to the closed environment of an oven. Every stove has different output burners (measured in BTU) and many stoves have burners with different outputs. Even then, stoves are not built with rocket precision so a 12,000 BTU burner may give you less output. Electric isn't much different, although it does offer greater precision once set.
Your best bets are as the other poster noted, an infrared thermometer to gauge surface temp on a hot pan or an probe-type thermometer to test meat or deep-fat temps.