It may be counterintuitive, but scientists have generally agreed that drinking a hot beverage can provide cooling relief for the body under certain conditions.

It may be counterintuitive, but scientists have generally agreed that drinking a hot beverage can provide cooling relief for the body under certain conditions, reports Quartz.
Ollie Jay with the University of Sydney explained to ABC News in 2015 that a warm beverage can cool the body but “the sweat needs to be able to evaporate to produce a cooling effect.” 
In one of his studies, the core temperatures of volunteer cyclists were tracked as they drank water at different temperatures. 
His research ultimately found that "because of the increased heat load from drinking a warm drink, there is a compensatory increase in overall sweat output that outweighs the initial heat gain. The more sweat that is produced, the more sweat that will evaporate from the skin surface, and this increases heat loss..."
Therefore, it is better to drink a hot liquid to cool down.
Neuroscientist Peter McNaughton also explained in a 2012 NPR article that when hot food or drink makes contact with a heat receptor in the tongue, the brain begins to activate the body’s sweat mechanism to cool it down.
He is quoted as saying, “The hot drink somehow has an effect on your systemic cooling mechanisms, which exceeds its actual effect in terms of heating your body.”