Cultural scripts can help structure collective remembering and future thought. This schematic scaffolding may help explain empirical patterns such as emotional biases in memory and future thought, as suggested by Liu and Szpunar (2023). In this commentary, we argue that the concept of “cultural scripts” as cognitive schemata shaping collective memory and future thought has been underspecified, such that cumulative theory building has been hampered. Here we outline some of the different schemata with which researchers have attempted to explain patterns in collective temporal thought. We contrast two major genres, ahistorical cultural schemata with historically contingent narrative templates. We then discuss two forms of narrative template, national narrative templates and implicit temporal trajectories. More precise specification of the “cultural script” concept will benefit researchers of collective temporal thought.