How, and what device do you need, to obtain the exact temperature of an open flame? For the purpose of this question, you wanted to maintain 375 degrees. You can control the flame, but have no idea the temperature of it. A pyrometer is probably the best device, but the evenness of the heat distribution is important. What do you use? Can a aluminum plate distribute the heat evenly? Is there a pyrometer that can reside, and attach, on top of the aluminum plate, i.e glued to the surface? What are other solutions to this problem?
A flame does not have a single temperature. The temperature at various points can be monitored using laser spectroscopy, or spectral measurements can determine the temperature of black-body emitters in the flame (soot particles). You will likely need a high degree of knowledge about the composition of the flame for these techniques, and probably this is not really what you want to be doing. More information on the problem you are trying to solve would be helpful.
As already stated a flame can have a wide range of temperatures depending on where you exactly measure it. As an example here is the rough temperature profile of a candle flame:
With a gas flame the temperature profile will be different but the general picture is similar. You can easily measure this profile with a Platinum or thermocouple thermometer that are needle shaped. If you are only interested in an average you can put a copper plate in the vicinity and measure the temperature of the copper plate and use that temperature to regulate your gas flow (might be very non-linear though).