Welcome to the group!
First off, there are no stupid questions that could be asked [posted] in this forum, so feel free to ask anything at all - even if it's non-electrical related. This applies to anyone reading / surfing the group.
As to the temperature ratings of the NM Cable [Romex], I'm almost completely positive that all NM Cable made since like 1995, or sooner, is rated for 90 degrees C. Max.
If this is incorrect, someone please reply to this message and correct it!
I very rarely use NM Cable, but have checked it out occasionly at Home Centers [Like the "Big Orange Box" - coining another person's nickname for The Home Depot]. The conductors inside appeared to have THHN insulation, plus the NM jacket appeared to be similar to the jackets of 90 degree C. rated cable that I used in the past.
I would verify the max. temp. by either checking the box it was in, or with the Manufacturer.
Now for the non-metallic connectors;
They will [or should] have a temp. rating labeled on them. The few I have dealt with in the past seemed to have a labeled max. temp. rating of 90 Degrees C., so verify this with a listed rating.
As to the deep boxes, your concern to the closeness of the cables in the back is valid, but not normally addressed as to the attachment to a stud would be. In other words, the typical restrictions of spacing cables is applied to where it lands on the stud, or other framing member, in relationship to it possibly being hit by a nail from drywall installation, lath installation or sheer panel installation.
I am sure that another person in this group can address this better and correct me where I am wrong, but I think there isn't any thing in the NEC restricting this part. Someone more apt to Residential work, or some of the Inspectors in the group, could verify this.
It's not that you couldn't try to do something to reduce the potential hazard - by all means please do!! Just because the NEC doesn't require something, or has little requirements for something does not mean that one couldn't try to make things a little more secure.
The NEC is first of all, the minimum requirements that are to be considered. The local codes [AHJ - Authority Having Jurisdiction], if more restrictive than the NEC, will need to be satisfied for full compliance. So Once again, the most famous catch phrase of these forums is used once again - "Verify This With The AHJ".
Secondly, the NEC is not a design manual or instruction booklet, it is just a set of agreed upon safety guidelines that are used to establish minimum safe installation requirements.
This simply means that you don't use the NEC to Engineer or Design a project's systems, but the installation it's self needs to be done within it's minimum requirements. Exceeding the minimums is quite fine, where as not meeting the minimums is a "no-no"
This once again might be incorrectly worded, so feel free anyone, to correct me.
Sounds like a bunch of "run around red tape" doesn't it
It begins to make sense after a little time!!
Since you are a DIY'er, please feel free to ask as much as needed before jumping into any project. We all appreciate this fact - you will get safe answers to go by [sometimes more than you expect
By all means, if something is too overwhelming to do, or is suggested by persons in the group not to be done by you, please seek professional assistance. Use a qualified and licensed electrician to help out on the heavy duty stuff, plus to check your installations if you have doubts.
We don't want to discourage DIY work performed by competent persons on their own houses, but we also don't want DIY'ers to go out and install things beyond their capabilities.
If Electrical installs are interresting to you, please extend your knowledge base with some books or classes.
Thanks for asking and once again welcome to the group! Hope to see you in the future.