I totally understand! There are a lot of us out there, we've discussed this before, actually. I took my fan but we had a storm and a small brown out and it killed it. We asked the front dest (we stayed at CSA) and they had one for us. If they couldn't find one for us, front desk had already phoned stores and had found one and had arranged a taxi to get us there.
We found ourselves so tired and spent at the end of each day that we fell to sleep almost instantly when we got to bed.
Well.... not right away. After some "activities" we drifted off quite nicely.
You could open the verandah doors or window a crack and enjoy the sound of the tree frogs. Many folks swear by them as a "white noise" diversion to get to sleep. There are some pretty small fans available that may fit into your suitcase. But I would just stick to the radio in the room or some other distraction. Maybe a glass of wine before turning in?
I'm so glad someone actually posted this thread!! My fiancé thinks I'm completely insane for trying to figure out how in the world to get our travel box fan on the plane. It will happen one way or another! The sound machine & tree frogs just don't compare & the AC fan is never loud enough.