Microcontroller units (MCUs) are often used in Internet of Things nodes that operate intermittently. Such nodes alternate active and inactive phases under strict energy constraints. Typically, the memory system has a significant impact on overall MCU energy consumption. Memory accesses and memory leakage power often dominate the consumption of active and inactive phases, respectively. Emerging Non-Volatile Memory (NVM) technologies have recently enabled the design of nonvolatile MCUs that can significantly reduce energy consumption during inactive phases. However, replacing all memories with emerging NVMs is not necessarily the best solution, as it often results in dynamic power overhead during active phases. Instead, a hybrid memory architecture that combines volatile and non-volatile technologies is a promising alternative. However, designing hybrid memory MCUs is challenging because the technology that best fits a data segment depends on its access pattern during execution (e.g., program memory experiences mostly reads while the stack alternates reads and writes). For a given intermittent application, our goal is to find the best memory architecture based on a data mapping that takes advantage of the different properties of the available memory technologies. To this end, we present MemCork, a tool for hybrid memory architecture exploration in intermittent computing devices. Based on an instrumented execution on a technology-agnostic FPGA prototype, our tool exhaustively explores the possible data mapping and memory architecture combinations to find the most energy-efficient solution. We evaluate MemCork on two representative intermittent applications and find a customised memory architecture and data mapping that reduces energy consumption by up to 23% compared to a fully NVM solution.