Just a single error line, but I just noticed this.

[main/ERROR] [campfirebackportmixins]: An error occurred when searching for the mod "Thaumcraft".

The crucible does not seem to be getting heated up properly. I expect this is also happening for the thaumatorium as well. TC support is enabled for the mod.

Thanks in advance for any help on the subject, this is the modlist I am currently using.
https://paste.ee/p/RdPwv

It might have something to do with SpongeMixins again.
Your modlist has SpongeMixins-1.3.1 but I can't seem to find a version above 1.2.0. Where did you get that version?

Oh, here http://jenkins.usrv.eu:8080/job/Sponge-Mixins/
And here's the repo for it https://github.com/GTNewHorizons/SpongeMixins though it is not currently supporting the ability to open issues

Thanks.
Unfortunately Sponge Mixins doesn't seem to be the cause, I can't replicate your issue.
I'm hoping that it's a more simple issue and isn't related to some weird mod interactions. I've made a couple changes, so can I ask you to be a beta tester?
https://github.com/connor135246/Campfire-Backport/releases/tag/v1.8.4-pre

Of course, thank you for taking time for this issue.

[main/INFO] [campfirebackportmixins]: Found "thaumcraftneiplugin-1.7.10-1.7a.jar". "Thaumcraft" mixins will be applied.

Hey looks like that worked! 👍
After actual testing, the cauldron heats up as intended.
Thanks again!