In order to run just a UTH the ambient temps in the room would need to be high enough.

Basically, your UTH only creates your hot spot. This is where your snake will tend to hang out during digestion after feeding. However, your UTH will barely affect your ambient temps, if at all.
So, unless the room where the enclosure will be kept remains at a pretty constant temperature of around 80 degrees you will need an additional heat source, also on a thermostat.