In this article, we propose an embedded cooling structure with thermal transmission line (ECS-TTL) to improve thermal integrity (TI) and signal integrity (SI) of a high-bandwidth memory (HBM) module. The proposed hierarchical cooling scheme, ECS-TTL, consists of ECS for lowering thermal resistance and TTL for smoothing thermal distribution. The ECS cools the module's integrated circuits by circulating fluid inside the computing module components. The TTL is a novel interconnection that focuses on transferring internal heat in a horizontal direction to achieve a uniform thermal distribution. The low and uniform thermal distribution achieved by the ECS-TTL can improve the temperature-dependent SI of an HBM module. We designed ECS-TTL by considering the structural reliability and SI of the HBM module based on its physical dimensions. We conducted TI verification of the HBM module by using a 3-D computational fluid dynamics solver; we evaluated the maximum temperature and the temperature uniformity of the HBM module with the proposed ECS-TTL and other cooling structures. Based on the TI evaluation, we conducted SI verification of the HBM by using a 3-D electromagnetic solver considering the operating thermal distribution; we evaluated the eye diagram and skew of the silicon interposer, through silicon via channels and a 3-D clock distribution network in the HBM. The evaluation verified that the proposed ECS-TTL can achieve a low and uniform thermal distribution while improving the eye diagram and skew of the HBM module compared to the conventional cooling structure.