I have calculated LST of Mumbai from Landsat (TM) image by two different methods. Final reults shows a difference of 0.24 degree celsius in both maximum and minimum temperatures. Is my result right?
Yes! It is quite common. No two different methods* yield same results in science. And the difference of 0.24 degree Celsius (in your case) says two methods are performed similarly.
However, I would suggest you to check with the ground based observations. You can use IMD or ISRO AWS data for validation.
I think that the most apropriate question to ask is about the best method to retrieve LST from Landsat images.
to answer this question, you have to compare the results with observed data. then, i think that the différence betweeen calculeted LST and measured surface temperature will be more than 0.24°C!!