Distribution locational marginal prices (DLMPs) have been formulated for electric distribution grids to economically dispatch distributed energy resources (DERs) while addressing operational constraints of the electric grid. This paper proposes to extend this methodology to thermal grids, i.e, district heating or cooling systems, and specifically the combined operation of thermal and electric grids. To this end, thermal and electric grid models are formulated in a linear approximate model fashion. Then, the derivation and decomposition of DLMPs is formulated based on the combined optimal operation problem, assuming a linear state space model form for flexible loads (FLs). The ability of the DLMPs to reflect operational constraints in the thermal grid is demonstrated for a test case with 22 FLs.