We investigate a SAT-based bounded model checking method for EMTLK that is interpreted over timed models generated by timed interpreted systems. In particular, we translate the existential model checking problem for EMTLK to the existential model checking problem for a variant of linear temporal logic, and we provide a SAT-based BMC technique for HLTLK. We evaluated the performance of our BMC by means of a variant of a timed generic pipeline paradigm scenario and a timed train controller system.