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• A public transit accessibility under heat exposure model is studied with time-dependent consideration. • A column generation method to urban rail-bus-walk service network integration is devised. • Experiments in Beijing show the impact of heat exposure on public transit accessibility. The evolution of urban transportation systems is increasingly driven by the integration of rail, bus, and walking pathways, forming a cohesive service network. This urban rail-bus-walk service network integration is pivotal in addressing urban challenges and ensuring seamless mobility. Nevertheless, the effectiveness of such integrated systems depends on their accessibility and the willingness of individuals to take them as their primary transportation mode. In the context of climate change, extreme heat events pose an increasing threat to passenger comfort and health, which in turn, affects individuals' decisions to use public transit. Additionally, walking to transit stops or waiting for transportation becomes more challenging during such extreme heat conditions. This paper tackles the challenge of comprehensively addressing the evolving issues related to public transit accessibility in response to rising temperatures, an area of research that has received limited attention until now. This paper introduced an approach aimed at optimizing the urban rail-bus-walk service network with a focus on both accessibility and heat exposure considerations. By calculating the transportation accessibility level under varying temperature conditions and identifying its vulnerability to high temperatures, this paper presents a methodology to enhance the transit service. Such improvement involves not only adjustments to the integration network but also considering of cooling facilities, such as shaded routes and shelters. Column generation is applied to solve this problem and the optimization result demonstrates improvement of accessibility under the extreme heat condition. [ABSTRACT FROM AUTHOR]