Climate shelters are critical urban infrastructures to support adaptation to extreme weather. They offer spaces – e.g., parks, libraries, and civic centers – where residents can take refuge during episodes of extreme temperatures. With over 200 public spaces designated as “Climate Shelters”, Barcelona (Spain) serves as an emblematic example of whether these emerging spaces are meeting the needs, expectations, and everyday experiences of the most vulnerable residents. By applying an intersectional climate justice perspective and mixed-method approaches rooted in a survey of a particularly climate-exposed working-class neighborhood (La Prosperitat), we found that the intersecting vulnerabilities of marginalized populations remain poorly addressed, largely due to differences in access to coping mechanisms that overlap with intersecting social positions, exacerbating vulnerability to climate risks. We also found that housing inadequacy and energy poverty experienced by low-income residents and those originally from Global South countries made them the most affected and least able to cope with extreme temperatures. Women were also more affected by climate impacts and more concerned about current and future risks. We argue that unequal lived experiences of thermal (dis)comforts inform heat and cold inequalities, which, in turn, are attributed to intersecting social positions and structural vulnerabilities. These uneven lived experiences shape – and are reshaped by – limited adaptive capacity, culturally inappropriate approaches, and insufficiently inclusive public spaces, thus complicating an equity-driven provision of refuge infrastructures. Results call for developing refuge infrastructures that address the intersecting social and climate needs of residents who need them the most.