My brother finally had to leave his Caribbean dream behind, in part because of the climate. His house was built by and for locals, so there was no way to air condition it (louvered windows, etc.). I visited him a few times, and while it was certainly bearable, it could get rather hot & sticky after a while.
He said the worst part after living there a while wasn't the heat, but the humidity, specifically the fact that you never felt dry. You would step out of the shower in the morning, and whatever residual moisture was left on your skin would just linger there until it was replaced by sweat.