Thermal IB-LBM implementation on a hot cylinder

Hi everyone.
Thank you so much for the platform.
I am working on thermal immersed boundary method. To start with, I attemp to simulate a hot cylinder in a channel using direct-force method. During calculation of boundary temperature and its effect on the flow, I encountered a problem through calculation and interpolation of boundary temperature. Should I define the boundary temperature Tb as Tb(boundary_counter) or based on Tb (xb,yb)???
I appreciate any kind answer.