Dual process theories of decision making describe choice as the result of an automatic System 1, which is quick to activate but behaves impulsively, and a deliberative System 2, which is slower to activate but makes decisions in a rational and controlled manner. However, most existent dual process theories are verbal descriptions and do not generate testable qualitative and quantitative predictions. In this paper, I describe a formalized dynamic dual process model framework of intertemporal choice that allows for precise, experimentally testable predictions regarding choice probability and response time distributions. The framework is based on two-stage stochastic process models to account for the two postulated systems and to capture the dynamics and uncertainty involved in decision making. As a proof of principle, I show how an existing static-deterministic model on intertemporal choice (Loewenstein et al. 2015) can be implemented in the framework allowing for testable predictions. The focus of the present paper is on the architecture of the two postulated systems: serial versus parallel processing. One serial and six quasi-parallel model versions are tested on data from Zhao et al. (2019).