Network densification via deploying dense small cells is one of the dominant evolutions towards future cellular network to increase spectrum efficiency. Packet transmission delay and reliability in the resultant interference-limited heterogeneous cellular network (HCN) are essential performance metrics for system design. By modeling the locations of base stations (BSS) in HCN as superimposed of independent Poisson point processes, we propose an analytical framework to derive the timely throughput of HCN, which captures both the delay and reliability performance. In the analysis, the BS activity and temporal correlation of transmissions are taken into consideration, both of which have significant effect on network performance. The effect of mobility, BS density, and association bias factor is investigated through numerical results, which shows that network performance derived ignoring the temporal correlation of transmissions is optimistic.