2 questions - new to ball pythons

[Basquet Ball Python]

Hello everyone,

I have a couple of questions as I am a new snake owner. My first question is regarding temperature. Where exactly should the temperature probe be placed for the heating mat? inside the tank or outside on the mat? I currently have it placed inside the tank and about a half inch underneath the substrate and its reading about 89 degrees. Also should I get a thermostat to regulate the temperature even if the temp has been consistently at about 89-90? And will a snake stay on the heat pad if its too hot or will move?

My second question is regarding taking my ball python places in the future. Not anytime soon, but when he is older and more comfortable is it ok to take him on short trips or in a tub take him over to my parents house for an hour to show them?

All advice is welcomed so please let me know. Thanks!