If the square is not part of the data set, you will need to create a new grid, ordered or finite element, that can be used to transfer the data you have through interpolation. If you compute the area of the cells in the original data, you should interpolate that data onto the new grid as well. Then, you can perform an integration based on a variable, or if you like, compute your own weights from the interpolated, scale the temperature, then perform the integration in steps. But to select a specific range of data,
Conversely, if the data you have is square in geometry, you can provide the limit of I, J, and K to determine the region you want to integrate. But as it stands, you still have to compute area/volume to have it area weighted. The issue is that you cannot specify a region to integrate within the Tecplot software.
Aerospace Research Engineer
NASA Langley Research Center