When reasoning about time, English-speaking adults often invoke a "mental timeline" stretching from left to right. Although the direction of the timeline varies across cultures, the tendency to represent time as a line has been argued to be ubiquitous and primitive. On this hypothesis, we might predict that children also spontaneously invoke a spatial timeline when reasoning about time. However, little is known about how and when the mental timeline develops, or to what extent it is variable and malleable in childhood. Here, we used a sticker placement task to test whether preschoolers and kindergarteners spontaneously map temporal events (breakfast, lunch, and dinner) and deictic time words (yesterday, today, tomorrow) onto lines, and to what degree their representations of time are adult-like. We found that, at age 4, preschoolers were able to arrange temporal items in lines with minimal spatial priming. However, unlike kindergarteners and adults, most preschoolers did not represent time as a line spontaneously, in the absence of priming, and did not prefer left-to-right over right-to-left lines. Furthermore, unlike most adults, children of all ages could be easily primed to adopt an unconventional vertical timeline. Our findings suggest that mappings between time and space in children are initially flexible, and become increasingly automatic and conventionalized in the early school years.