Preventing Health Emergencies And Temperature-related Illness and Deaths Act of 2021 or the Preventing HEAT Illness and Deaths Act of 2021 This bill provides statutory authority for, and otherwise revises, the National Integrated Heat Health Information System Program to improve the capacity of the United States to prepare for, adapt to, and mitigate health risks of extreme heat. The Office of Oceanic and Atmospheric Research of the National Oceanic and Atmospheric Administration (NOAA) must carry out this program. (Currently, the program is jointly administered by NOAA and the Centers for Disease Control and Prevention.) Under the bill, the program may provide financial assistance for projects to increase awareness, education, and research about extreme heat events and mitigate the human health impacts of those events. In awarding the assistance, the program must prioritize historically disadvantaged communities and communities with significant heat disparities associated with race or income. Other components of the program include grants for research on climate and health and a study of relevant policy, research, and data gaps concerning extreme heat information and response. The bill also establishes an interagency committee within the White House Office of Science and Technology Policy to develop a strategic plan and otherwise coordinate federal activities related to the program.