Re: At -179C
Yes, the smallest gap between ambient temp and the HC boiling point should be at the surface, If the sub never has to surface1 the designers could work on a larger heat budget. But we don't know the actual temperature gradient as depth increases so there's also the possibility that the sea is slightly warmer at depth for whatever reason and gap actually narrows2.
There is the possibility that the first subs entire mission is a one way dive calling out temp & density as it plummets, that alone would be a major achievement in data gathering and pretty much guarantee sub#2 has a good operational envelope.
Basically the engineering for this first sub will be a best educated guess dive into the unknown based on distant observations and fly-bys as all first of type probes have been (This one is likely to be the first into liquid).
1I'm guessing at a tethered buoy with radio relay equipment for data transfer.
2Accurate calculations can't be made without detailed information about actual temperatures & densities, they're something the sub itself will need to collect.