Intertemporal preference has been investigated mainly with a choice paradigm. However, a matching paradigm might be more informative for a proper inference about intertemporal preference and a deep understanding of the underlying cognitive mechanisms. This research involved two empirical studies using the matching paradigm and compared various corresponding dynamic models. These models were developed under either the framework of decision field theory, an exemplar theory assuming evidence accumulation, or a non-evidence-accumulation framework built upon the well-established notions of random utility and discrimination threshold (i.e., the RUDT framework). Most of these models were alternative-based whereas the others were attribute-based ones. Participants in Study 1 were required to fill in the amount of an immediate stimulus to make it as attractive as a delayed stimulus, whereas those in Study 2 needed to accomplish a more general matching task in which either the payoff amount or delay length of one stimulus was missing. Consistent behavioral regularities regarding both matching values and response times were revealed in these studies. The results of model comparison favored in general the RUDT framework as well as an attribute-based perspective on intertemporal preference. In addition, the predicted matching values and response times of the best RUDT model were also highly correlated with the observed data and replicated most observed behavioral regularities. Together, this research and previous modeling work on intertemporal choice suggest that evidence accumulation is not essential for generating intertemporal preference. Future research should examine the validity of the new framework in other preferential decisions for a more stringent test of the framework.