RIO DE JANEIRO — What it lacked in flash, Rio made up for with feeling. With a limited budget, the consequence of a biting recession that roiled preparations for South America’s first Olympics, Brazil laced its high-energy opening party for the games of the 31st Olympiad with a sobering message of the dangers of global warming. Graphic projections of world cities being swamped by rising seas set Rio de Janeiro’s otherwise fun and festive gala apart from the more self-congratulatory and lavish celebrations that Beijing and London wowed with in 2008 and 2012. “The heat is melting the icecap,” a voice intoned in the Maracana Stadium.