Use MATLAB

I had similar research on LST versus distance for Landfills. I wanted to know how LST changes along with the distance from the landfills. For this purpose, I used euclidean distance in Arcgis and assigned a raster map for an area. Once it is extracted, I combined the results with LST and extracted the multi values to points, once it is clarified, I had an attribute table which included LST and distances in two different columns. Therefore, you can extract the attribute table as dbase file and import it into an excel sheet.

@Nima Thankyou for your valuable suggestion, I'll surely incorporate this advice in my work.

You can use buffer analysis of that. Take a middle point in the city and then create fine equal buffer inter and then calculated the mean LST and of each buffer and the plot the distance on X-axis and mean LST on the y-axis.