My Pekin ducklings went through a mouth breathing/panting phase around that age and I'm fairly certain most of them went through a heavy sneezing phase. Like they'd do a bunch of sneezes in a row several times a day. None ever acted "sick" though so I tried not to worry. I'm guessing those tiny downy feathers might just tickle their sneezers sometimes. 
As for the panting/heat issue, I'm not sure about all duck breeds but I know from snuggling experience that Pekins do get hot at a young age. My super spoiled baby (crazy to imagine that one is more spoiled than the rest considering how spoiled they all are), Bill Bill, loved to snuggle when he was small and I was amazed by how overheated I'd get having him lay on me. The weird thing I've noticed with mine is even though they're panting and have plenty of space to get away from the heat lamp if they want, they will often choose to lay under the light. They move away or go get water if they're too hot. I'm pretty sure my two youngest Pekins are around the same age as yours. Right now one is snuggled under a lamp and the other is across the room away from the light. My adult ducks seem to do this outside too, only not with a heat light obviously. Some will lay under trees in the shade while others will stay stretched out in the sun even when they're panting. I figure some just like being extra warm like a dog I used to have. She would stretch out in from of the fireplace, so close that her belly would turn red and she'd pant like crazy. If I moved her she'd pout like she was being punished. Critters are just weird sometimes.