I can tell you now, you can not tell what temp that heat mat is by the touch. Unless you are holding your hand to it constantly. They fluctuate terribly, and you have to account for the temp of your house.
This is why a dimmer/thermostat/rheostat is required (not recommended, but required with all heat mats). Dimmers are fairly cheap at any hardware store. They aren't hard to hook up either. I don't understand why you don't want to use it.
If you have a heat gun, have you ever tested her cage since you brought her home? You can even get a thermostat from Amazon for $30.
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