What are the temperature and pressure conditions an ROV design would have to deal with to descend to 4000m?
For pressure, you can use something simple like the fact that pressure increases by around 1 atm with each 10 m of water depth. You can also use some very simple calculators that assume a constant density (not a bad assumption) and gives you the different unit conversion.

For temperature, it varies a fair amount depending on where in the ocean. The average vertical profile for mid-latitudes, looks something like:

 (Windows to the Universe).

If you need more detail temperature information for a specific location, you can look into the World Ocean Atlas, which provides observed temperature, salinity (and in some cases other parameters like ph) for the entire world.

My suggestion is that, if you need any specific information, you might ask the people at the Woods Hole Oceanographic Institution (for instance) that deal with this kind of problem on a regular basis.