Pain can cause stress, and stress typically raises temperature. I’d say a thermometer is a very good tool but it won’t really offer a diagnosis. It has many practical uses though.

First of all it’s very good to establish a baseline temp. Just as with humans and dogs (and probably other mammals as well), normal temp varies somewhat between individuals. If you know what her normal temp is when she’s healthy, it’s easier for you (and your vet) to know when sth is off, based on her temp. Keep in mind that body temp varies over the day and with the bun’s activity level.

If your bun should stop eating etc, it’s very useful to know if she has a low temp, because if she does, she must be warmed up until you can get to a vet.  For this reason it’s good to always have hand warmers or a heating pad in the bunny first aid kit. Buns can easily get hypothermic if they are poorly, and that’s very dangerous for them. Rabbit painkillers, often given when a bun has tummy trouble as an important part of stasis treatment, lower the body temp, making it extra important to keep an eye on the temperature.

Obviously a very high temp (fever) means there’s some sort of infection or other serious problem. A slightly higher temp can signify stress, as previously mentioned.

Its good to practice taking your buns temp, but don’t practice so much that she gets stressed out (obviously). I’ve found this video very useful: https://youtu.be/YZd10Hk0maA

If you can keep him more upright that will prevent him from trancing.