A combustion furnace is quite a complex environment from the heat transfer viewpoint. The combustion mass contains radiating solids and gases, as well as diathermic (infrared radiation-transparent) gases.
As for the temperature reading error, it all depends on the radiating enclosure; for example, whether the measuring thermowell "sees" a radiating flame or just cooler walls and tubes.
If we call temperatures
T1: the true gas temperature
T2: the temperature reading
T3: the enclosure temperature
T1-T2 = [Δ]T: the error
I think we could say that in the radiant section, where radiating flames are "seen" by the thermowell, T3>T2 [≥] or [≤]T1, while in the convection section, T1>T2>T3.
As hacksaw says the convection heat transfer coefficient, hc, would be small in comparison with the radiant one, hr, at ~ 1100oC. Thus hT = hr + hc [≈] hr.
Have a look at Holman's Heat Transfer example 8-11 for an illustration. The exercise refers to air and a bulb thermometer, but it could also be applied to a thermocouple in a ceramic thermowell. The example refers better to the case of gases in the convection section.