As a vital component of urban heat risk, the vulnerability of exposed elements must be assessed before further impact prediction and strategy implementation. In previous studies, heat vulnerability was commonly defined as the tendency to be adversely affected by an extremely high temperature from both physical and social perspectives. However, it cannot explain what the adverse effects are. Also, the decision-making of mitigation strategies was often regarded as an individual section, lacking a combination of heat vulnerability. This paper established a qualitative multi-sector network by discovering existing cause-effect within indicators related to heat vulnerability, extending the concept of vulnerability. It identified what makes population and urban elements vulnerable to urban heat from the view of the effects they trigger. Besides the physical and social sectors of demographic, urban elements and exposure, three essential but frequently ignored effect sectors - emissions, human health, and economy - were also included in the causal network. Based on a new classification of mitigation strategies, they could connect with vulnerability indicators in multi-sectors, forming causal chains from intervention to their profound effects. A discussion of the network's future implementation was conducted in the end, prospecting the potential of a combination with the vulnerability assessment. This paper uncovers that future vulnerability assessments should include productivity as an indicator to show the adverse impact of high temperature on the economy. It also shows that different mitigation strategies can intervene in heat vulnerability assessment through all cause sectors, the sector of exposure, and the sector of emissions.