I will define the heat Eisenstein series and sketch some of their theory, as developed by Jorgenson and Lang in the 90s and early 00s. Then, I will describe their role in an ongoing project to generalize theta relations and spectral zeta functions to arithmetic quotients of real Lie groups in higher rank. Finally, I will state some of my results on exact fundamental domains and explain how they are used or are expected to be used in this program.