Keeping your ambient temp at 80 or 84 is not a fire hazard however it will definitely increase the bill.

There are other options it all depends on your needs

I have a snake / leopard geckos room and it is kept at 80-82 year round (of course I have more than just 2 snakes)

If you only have 1 or 2 snakes having the whole room heated at 84 might not be the most cost efficient way to do it.

Here are some ideas

If you have glass tank you can switch to tubs

You can insulate your enclosure

You can use 2 UTHs (1 on each side) and 2 Thermostats one set to provide 80-84 and the other set to provide 90-94.

Ultimately find the solutions that help you provide the proper temps for your animal and that your parents approve of.

And remember you are very fortunate to have parents allowing you to own reptiles, just communicate with them and explain what your animal needs how and how you can achieve them.