So I take it I should try and cool the exhausted air as is come out of the tent before it excites the shed ??
Not sure how you will go about that but a hot air exhaust coming out of a shed would be a red flag.
They have busted grow houses because of seeing heat plumes coming from under homes, out of odd places where heat normally isn't produced, seeing a bed room thats 85F when the rest of the home is 75F. If you used an AC unit, thats going to look weird on a shed and the condenser unit will show the heat.
One way or another you need to move heat out of the grow space, an undetectable way eludes me. Even a trenched exhaust piped to another place would have to be deep to prevent them from seeing a hot line on the ground leading from the shed to the vent with it's associated heat plume.
About the best possible solution I can come up with is a heat exhanger on the exhaust. This would use air flowing in from the outside to temper the exhaust heat but it still won't remove all the heat and your intake air is now pre heated so that would suck.
I can't think of a solid solution.