The OP is NOT speaking of a tank. A plastic tub has next to no insulative value. There is likely to be little loss of heat to the tub so you are relying on just the (MOVABLE) substrate to protect the OPs snake. That is irresponsible. I might concede that a UTH on a tank with carpet and rocks might not exceed 100šs but that is NOT what was described. You do understand that Royals cannot digest food if their core temp is to high or too low right? The OP does not have regulated rooms or over head heat just a single snake and a plastic tub. Even if you don't need a t-stat (I disagree but...) he/she does.
Thermal burns are the NUMBER ONE injury for captive reptiles. Thermostats are the primary defence against this occurring. Cycling a resistive heater should do less harm that running it 100% 24/7.