The heat mat plus the lamp might have been overkill. Once again I recommend getting a thermometer to check the temperature if you don't have one.
Also, kind of a minor side note since it probably didn't cause your frog to die, reverse osmosis water isn't very good for frogs. Sometimes bottled spring water is treated by reverse osmosis, but they generally add minerals back to the water. Tap water treated with dechlorinating drops (usually) is fine.
http://www.caudata.org/cc/articles/Spring_water.shtml