  The temporal evolution of Kuramoto oscillators influenced by the temperature
field often appears in biological oscillator ensembles. In this paper, we
propose a generalized Kuramoto type lattice model on a regular ring lattice
with the equal spacing assuming that each oscillator has an internal energy
(temperature). Our lattice model is derived from the thermodynamical
Cucker-Smale model for flocking on the 2D free space under the assumption that
the ratio between velocity field and temperature field at each lattice point
has a uniform magnitude over lattice points. The proposed model satisfies an
entropy principle and exhibits emergent dynamics under some sufficient
frameworks formulated in terms of initial data and system parameters. Moreover,
the phase-field tends to the Kuramoto phase-field asymptotically.
