Many people have worked on this problem since the game launched (and maybe before then). We have had many threads on this topic, but we still don't know the exact algorithm.

People have studied the effects of damage type (vulnerable, neutral, resistant) and damage bonuses (+0, +1, ..., +6), and we have extensive data, for example here and here. For example, we know that each level of damage bonus increases damage by about 5%. But there are some instances in which it increases damage by 7% or 8%, and it seems to depend on damage type. So the damage calculation is surprisingly subtle. See here for more detail on damage type.

For your specific problem, look up Divine Avenger on the wiki. Look at the largest numbers for Stratum 3, which represent depth 12. Also look at the smallest numbers for Stratum 4; they represent depth 14. Your depth 13 numbers should be in between those. You can also do direct tests at a Tier-2 guild training hall.

Heat is a very temporary problem; once you play with a weapon for a little while, it gets fully heated and stays that way forever. So all damage numbers on the wiki are collected at heat level 10. Do not hold your breath, waiting for people to analyze how heat affects damage in any thorough way.