I would be surprised if there was a software package that could (easily) do what your asking for. Even a simple climate calculation depends on a large number of factors that make modelling it really quite difficult. (I am understating this quite a bit!)
However I think you can do a lot with a bit of knowledge and using some very basic simplifications that do take into account the physics of the situation.
Have you seen the Youtube channel
Artifexian?
He talks about building worlds to the level that I think you want, but doesn't use a supercomputer nor any modelling software to construct them. But, with my physicist hat on, I can vouch for the information and ideas that he uses. At least for the videos that I have watched!
See, for example:
(note, in this video he is talking about Koeppen classification, but states that you need your landmasses, ocean circulation and other factors before embarking on trying to work out what your climate zones will be.)
If you go into his playlists you can see he has about 60 short videos on worldbuilding on a large variety of topics that may be helpful for you. He also had a recent excellent series on how to draw some great looking maps. Hopefully some of it may be useful.
If you are thinking of making your world very different from an Earth-like planet this may not be enough, but use his vids as starting points for further research to try and estimate what would be different for your non-terran world.