sounds like your harvest and curing techniques are ok.
i would not store garlic in an area that is above 70 degrees for any length of time and forget 100! i think the heat is drying out your garlic, it'd dry me out being in that garage!
apparently you live in a hot climate. do you have a basement that is dry and cool? do you a/c your house? if so maybe a room or closet where the a/c keeps the garlic 60-70 degrees? if no basement, no a/c and outside temps are always 80+ i don't know what to say.
a fridge will encourage them to sprout after a while. your root cellar may work but it can't be damp, most root cellars are damp for storage of crops that require cold and humidity.
if you can't find anywhere to store them i'd suggest contacting karen or mike at
http://wegrowgarlic.com and ask for their recommendation about storage. also ask what varieties they'd suggest growing that would be more appropriate storage-wise for your climate. perhaps there are varieties that store in hot climates tho garlic originated in cold climates so it may only store for a few months in really warm climates. you could move to a temperate climate for the cold.
tom