On many dairy farms cows are kept indoors. Providing outdoor access is often considered desirable, but housing can protect animals from aversive climatic conditions. For example, by providing shade and fans, indoor housing can protect cows from heat stress they might otherwise experience on open pasture. This study tested how public attitudes to cattle rearing varied when participants were experimentally assigned to different scenarios using a 2 x 2 factorial design varying pasture versus indoor housing with or without heat stress. Participants (n = 581) were randomly assigned to a single scenario, and attitudes in response to the scenario were measured using a Likert scale (1 = "strongly disagree" to 5 = "strongly agree"). We also asked open-ended questions allowing participants to explain their responses. Participants responded most positively to the scenario that provided both pasture access and protection from heat stress (Likert 4.1±0.08), and least positively to scenario with indoor housing and heat stress (Likert 2.2±0.08). However, when the different animal welfare attributes were in conflict (i.e. naturalness as provided by pasture, and biological functioning/affective state as associated with protection from heat stress), participants placed priority on the latter: they were more supportive of the scenario providing indoor housing that protected cows from heat stress (Likert 3.5±0.08), than they were of a pasture rearing system that exposed cows to heat stress (Likert 2.4±0.08). Open-ended responses indicated that participants viewed the lack of protection from heat stress as a failure in the farmer's duty of care towards the cow. We conclude that participants valued both access to pasture and protection from heat stress for dairy cows, but prioritized protecting animal from heat stress when these features were in conflict.