New York City officials have declared a heat emergency and opened roughly 500 cooling centers as the season’s first major heat wave settles over the region. The network of libraries, community centers and senior facilities is intended to give residents without air-conditioning a safe place to cool off. The National Weather Service placed the city under an Extreme Heat Warning from Sunday through at least Wednesday, forecasting air temperatures near 100°F and heat-index readings above 100°F. Municipal agencies warned that the stretch could rival the hottest conditions recorded since 2012 and reiterated that heat is the city’s deadliest weather hazard. Health authorities said more than 500 New Yorkers died prematurely from heat-related causes last year, underscoring the risks for older adults and people with medical conditions. Residents are urged to use air-conditioning whenever possible, drink water frequently, limit outdoor activity and check on vulnerable neighbors or co-workers. Cooling-center locations and hours are available by calling 311. Similar measures are being taken across the Northeast and mid-Atlantic. Massachusetts activated an Extreme Heat Warning, Washington, D.C., extended its Heat Alert through Thursday, and Baltimore issued a Code Red advisory. The National Weather Service cautioned that dangerous temperatures will persist across much of the eastern United States through the week.