I'd probably recommend a combination of two solutions:
1: The above Thermocube with a space heater.
2: A dehumidifier. Not the ones that use a peltier system and remove water from the air by the teaspoon, but the ones that have a compressor, use 800-1500 watts, and yank it out by the pint.
From there, leave a vent open.
One person I know made a box that fits atop his roof vent that has filters on all sides (and is rain resistant.) He then runs the fan in reverse, pulling air in during the Texas summer. This not just keeps the dust and sand at bay, but insects like mosquitos and moths tend not to be able to get in due to the positive pressure out the windows and cracks.
