An understanding of the long-term thermal evolution or thermal history of magma storage is key to understanding the behavior of crustal magmatic systems. The ability to measure both age and crystallization temperature in zircon crystals is increasingly being used to infer the thermal history of magmas in young volcanic rocks. However, the temperature dependence of zircon crystallization and the effects of analytical uncertainties also affect the ability of zircons to uniquely record thermal variations during magma storage. We have developed a probabilistic forward modeling approach to explore zircon age—crystallization temperature systematics produced by user-generated thermal histories. Results suggest that zircon data sets acquired by secondary ion mass spectrometry currently have limited ability to uniquely resolve magmatic thermal history. Uncertainties in measured ages are typically longer than both the time taken for zircon growth at the analyzed scale (∼1–20 µm), and the expected duration of thermal rejuvenation events. This strongly limits the extent to which short thermal pulses can be distinguished. Episodic and continuous temperature histories produce remarkably similar zircon systematics, particularly when sample sizes are small. Natural zircon samples that show a range of apparent temperatures through time, and that have been interpreted to reflect extended magma storage at relatively elevated temperatures, can also be produced by near-solidus magma storage punctuated by a limited number of short thermal rejuvenation events.