Building Controller Display Screen or Portion Thereof with Graphical User Interface

FIG. 1 is a front view of a building controller display screen or portion thereof with graphical user interface;

FIG. 2 is a second embodiment of a building controller display screen or portion thereof with graphical user interface;

FIG. 3 is a third embodiment of a building controller display screen or portion thereof with graphical user interface;

FIG. 4 is a fourth embodiment of a building controller display screen or portion thereof with graphical user interface; and,

FIG. 5 is a fifth embodiment of a building controller display screen or portion thereof with graphical user interface.

The outer most broken line in each of FIGS. 1 - 5 represents a boundary of the building controller display screen, and form no part of the claimed design. The broken lines showing portions of the graphical user interface form no part of the claimed design.