Solnit (In A paradise built in hell: The extraordinary communities that arise in disaster. Penguin 2010) notes that it is often the case that immediately after a disaster occurs, voluntary mutual help motivated by altruism among the victims is observed. She names this phenomenon "a paradise built in hell." Subsequently, it has been pointed out that "a paradise built in hell" has the potential to reform existing social institutions in the long term. Through the application of a social network model based on game theory, this study models the link formation motivated by altruistic preferences during disasters and analyzes the possibilities for a long-term outcome induced by the short-term effect of "a paradise built in hell." More specifically, we utilize numerical simulations and examine the dynamic effect of altruistic link formation during disasters on the properties of a network such as network density and disparities in the number of links of each player. In addition, this study focuses on larger-scale disasters that lead to more instances of altruistic behaviors among affected people, and analyzes such behaviors' cross-sectional and dynamic effects on social welfare as well as the possibility of the long-term outcome of "a paradise built in hell."