Green hydrogen plays a pivotal role in the imminent energy transition, addressing energy storage and electricity generation decarbonization. The European Commission's hydrogen strategy underscores the goal to install at least 40 GW of green hydrogen electrolysers by 2023. Despite various electrolyser technologies, efficiency improvement and durability enhancement remain challenges, especially considering voltage intermittencies from renewable energy sources. This study emphasizes the impact of thermal gradients within electrolysers due to voltage interruptions, affecting membrane operation and causing premature wear. The study explores methods to minimize thermal gradients, revealing trade-offs between efficiency and durability. A lumped-parameter numerical model is developed and experimentally adjusted to simulate electrochemical and energy transport phenomena. Experimental and numerical results are compared, highlighting the need for a comprehensive thermal management code for effective electrolyser performance. The study addresses the importance of accurately modelling transient thermal responses for both proton exchange membrane electrolysis (PEMEL) and solid oxide electrolysis (SOEL) designs, providing insights for future advancements in thermal management strategies.