Definitely get a digital thermometer with probe and put it under substrate like KMG said. Even though the tub doesn't feel hot doesn't mean it isn't. As humans our body temp is higher then bp hot spot so normally it wouldn't feel hot unless its actually hotter then our body temp. If you walked outside for 20 mins in 20 degree weather and came back in and touched it then it would feel hot due to your body temp being lowered from being outside.
I use lamp dimmers and yes like KMG said you do have to keep an eye on them due to the changes in temp in your home. I'm constantly monitoring temps so its not a big deal to me. I would be checking all the time with 3 temp guns in all my herps enclosures even if I did have a thermostat. I want to upgrade and get a few herpastat 4s but the price drags me down a little. Especially bc I need 3 of them.