Find light bulb surface temp from temperature measurements

[dons33]

Homework Statement

I have 3 data points of steady state temperature at 3 locations some distance away from a bulb, I need to calculate the temperature of the surface of the bulb. It would be best to assume the bulb is a hemispherical radiation source, based on the experiment set-up

Homework Equations

q^''=σ(Ts-Tsurr)⁴
I=E/∏
G=I∏

q=kAΔT

The Attempt at a Solution

I am assuming the temperature distribution is not linear so using a line to fit the data then backing out the temp would not give an accurate result.

 

[mfb]

I don't think that will work at all.
If you can find a reasonable shape for the temperature distribution (based on a simulation or whatever), you can fit it - it is certainly not a straight line, but that does not matter for the fit.