Energy 3D printing processes have enabled the manufacturing of energy storage devices with complex structures, high energy density, and high power density. Among these processes, freeze nano printing (FNP) has risen as a promising process. However, quality problems are among the biggest barriers for FNP and other 3D printing processes. Particularly, the droplet solidification time in FNP governs the thermal distribution and subsequently determines the product solidification, formation, and quality. To describe the solidification time, a physical-based heat transfer model is built. But, it is computationally intensive. The objective of this work is to build an efficient emulator for the physical model. There are several challenges unaddressed before: (1) the solidification time at various locations, which is a multi-dimensional array response, needs to be modeled and (2) the construction and evaluation of the emulator at new process settings need to be quick and accurate. Here, we integrate joint tensor decomposition and nearest neighbor Gaussian process (NNGP) to construct an efficient multi-dimensional array response emulator with process settings as inputs. Specifically, structured joint tensor decomposition decomposes the multi-dimensional array responses at various process settings into the setting-specific core tensors and shared low-dimensional factorization matrices. Then, each independent entry of the core tensor is modeled with an NNGP, which addresses the computationally intensive model estimation problem by sampling the nearest neighborhood samples. Finally, tensor reconstruction is performed to make predictions of the solidification time for new process settings. The proposed framework is demonstrated by emulating the physical model of FNP and compared with alternative tensor (multi-dimensional array) regression models.