Test-time scaling has recently emerged as a promising approach for enhancing the reasoning capabilities of large language models or vision-language models during inference. Although a variety of test-time scaling strategies have been proposed, and interest in their application to the medical domain is growing, many critical aspects remain underexplored, including their effectiveness for vision-language models and the identification of optimal strategies for different settings. In this paper, we conduct a comprehensive investigation of test-time scaling in the medical domain. We evaluate its impact on both large language models and vision-language models, considering factors such as model size, inherent model characteristics, and task complexity. Finally, we assess the robustness of these strategies under user-driven factors, such as misleading information embedded in prompts. Our findings offer practical guidelines for the effective use of test-time scaling in medical applications and provide insights into how these strategies can be further refined to meet the reliability and interpretability demands of the medical domain.