Well it is going to dry extremly fast. I'm assuming you know high temps drys it out faster, and low temps slow down the drying process.
And i'm sure you know its the opposite with humidity as you mentioned low humidity. Low humid dry faster. High humid dry slower.
Also temps over 75 I think is what will degrade thc. I'm not sure, but a box would let the humidity build up. As well as raising temperature. Though being in a tent with the box and the sun beating on the tent rather than the box the box will probably be cooler than the tent air.
I think high humidity and high temperature hugely increases mold risk. Moreso than say high temp and low humidity, or low temp and high humidity.
You could make a shade to shade the tent, and as I mentioned the box would probably let the humidity build up in a smaller space as well as it being paper would soak up some moisture.
These next suggestion is just a thought I had, but like a shade you could put wet towels on the tent? This is probably a bad suggestion.
You have a hygrometer right? At the least wal-mart should have an Acu-Rite temp, and hygrometer for 9$. Its over beside paint, and guns somewhere.
Why dont you want to bring them inside? An A/C unit will bring down temperature, and humidity. Mine puts the room in the optimal dry zone.
How much do you know? People will put a pan with water in the area to raise humidity. Though I'm not sure if its better to just dry fast with those temperatures it would seem like it. Prolonging the dry might be counterproductive. The temp is probably more a factor than the humidity.
Someone else will give you a better shorter answer though.
Your not going to bring it inside for the cure thpugh, right?