A thermostat can be used to regulate multiple heat sources if they are all the same type (including size and wattage). One t-stat won't work for both the lamp and the UTH, unless it has two separate inputs.
The UTH should not be always on, they can get hot enough to burn your snake in minutes if they run unregulated.
Personally I would ditch the lamp completely and just use the UTH for heat, the lamp just kills your humidity anyway. Put a hide over the UTH and it will trap heat underneath for a warm area, and cover the whole top with plexiglass to keep humidity in.









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