An pulsed heating atomic layer deposition (PH-ALD) technique is used to grow heteroepitaxial ZnO thin films on -plane sapphire with temperature-sensitive metalorganic precursors. During metalorganic precursor delivery, the substrate is maintained at a base temperature of 110 °C to prevent thermal decomposition of the precursors. After the substrate is sequentially exposed to the metalorganic precursor and water co-reactant at this low temperature, a high-power resistive heater is used to rapidly heat the substrate to between 400 and 900 °C to drive film crystallization. These heat pulses enable epitaxial growth of (0001) ZnO films on -plane sapphire. Rocking curves with FWHM of values as low as 0.53° are achieved. In contrast, films deposited entirely at 110 °C appear random polycrystalline and post-deposition annealing to 900 °C achieves only partial "epitaxial character" with a notably different in-plane orientation. Variations in heat pulse temperature and the number of deposition cycles between heat pulses are explored. Epitaxial growth persists up to 5 deposition cycles per heat pulse, with the 2 - FWHM increasing to 1-2°. To further reduce process times, a templating approach is also explored in which a limited number of "template" layers are initially deposited with PH-ALD followed by low-temperature ALD at 110 °C. Epitaxial growth is encouraged with as few as 5 cycles of PH-ALD followed by 495 cycles of low-temperature ALD. Crystal quality further improves by using up to 50 template cycles, with a 2 - FWHM of 1.3°. Epilayers also show enhanced photoluminescence (PL) at room temperature. These results demonstrate how pulse-heating can be used to promote epitaxial film growth in ALD processes using temperature-sensitive metalorganic precursors.