I'm not sure whether that is a 'yes' or a 'no'! Can you clarify whether or not you're suggesting that more heat would be generated with, say, 6.5A being drawn through each output of a double socket as compared with 13A being drawn from a single socket?Whether it is single or double there is only one terminal each for live and neutral cables and the entire current has to pass from the barrels of these terminals to the interconnecting strips and this is ( most likely ) the main source of heat
Kind Regards, John