The production of hydrogen through water electrolysis has emerged as a promising alternative to decarbonizing the energy sector, especially when integrated with renewable energy sources. Among the key operational parameters that affect electrolysis performance, temperature and current density play a critical role in determining the energy efficiency, hydrogen yield and durability of the system. The study presents a Systematic Literature Review (SLR) that includes peer-reviewed publications from 2018 to 2025, focusing on the effects of temperature and current density across a variety of electrolysis technologies, including alkaline (AEL), proton exchange membrane (PEMEL), and solid oxide electrolysis cells (SOEC). A total of seven high-quality studies were selected following the PRISMA 2020 framework. The results show that high temperatures improve electrochemical kinetics and reduce excess potential, especially in PEM and SOEC systems, but can also accelerate component degradation. Higher current densities increase hydrogen production rates but lead to lower Faradaic efficiency and increased material stress. The optimal operating range was identified for each type of electrolysis, with PEMEL performing best at 60–80 °C and 500–1000 mA/cm², and SOEC at >750 °C. In addition, system-level studies emphasize the importance of integrating hydrogen production with flexible generation and storage infrastructure. The review highlights several research gaps, including the need for dynamic modeling, multi-parameter control strategies, and techno-economic assessments. These findings provide a basic understanding for optimizing hydrogen electrolysis systems in low-carbon energy architectures.