Hi Myca!
You can place the UTH directly under the plastic tub, attached to a thermoSTAT, which will regulate your UTH temperature so you have no worries about the plastic melting! You'll want your temp. to stay consistently around 86. Some UTH's get upto 120 if they are not regulated.
You can get a thermometer at the petstore. You place the probe on the inside of the tub, directly on the plastic above the UTH, which will be on the outside underneath.
This will tell you your temps.
You're definitely not ignorant, this is all part of the learning process, we've allll been through it. I personally have my snakes in glass viv's, but I know theres many members on here that use plastic tubs within rack systems. You will definitely get more in depth advise on how to set up your plastic tub best if you ask in the husbandry thread
I want to get a Mexican black kingsnake, and plan on housing him in a plastic tub aswell, so I'm learning the best "How-to's" also