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I suspect a lot of good work has been done that is published on what a fire looks like across the visible and invisible spectrum. If putting the fire out is the objective then you'll need to differentiate between things heated by the fire and the fire itself. I think Fire Science might be the right term to describe the area where you might find the best info - possibly some fire science journals. At a distance the simple sensors will give you some kind of initial direction but as you get closer to anything much larger than the flame of a candle the sensor may not provide enough information to keep you centered. Too general a sensor might become blind or be overwhelmed at a practical distance for a robot.
Before thinking that a little research is overkill - you might find that the part of the fire that interests you emits a lot of one wavelength or another. A low cost photocell with the right plastic filter might actually work out quite well - either in addition to or instead of the general heat sensor.
Not sure where you live but many of the people we call Fire Marshalls who work in urban areas have fire science background. A call to one might prove to be worth the time. If this is for a school project they are often more than willing to assist.