Burst firing in thalamic reticular neurons is key to sleep rhythms and is linked to neurodevelopmental disorders. Several models of reticular neurons are currently available; however, a biophysically detailed model reproducing experimental burst firing heterogeneity is lacking. We addressed this by combining patch-clamp electrophysiology of fluorescently tagged Spp1+ and Ecel1+ neurons with a previously established statistical framework to differentiate cell types. We developed a population of biophysically detailed thalamic reticular models capturing diverse firing properties, particularly varied rebound bursting. These models incorporate key ion channels, such as T-type Ca2+ and small conductance potassium channels (SK), allowing systematic study of their impact on single-cell dynamics. By integrating these models into a thalamic microcircuit, we demonstrate that T-type Ca2+ and SK channel conductances have opposing effects on spindle oscillations. We identify a simple relationship between these conductances and spindle peak firing frequency, and provide a foundation for relating cellular properties to network activity.