I think that the basic idea is that there are going to frictional losses of HP in the gearbox. Most people state this as a percentage of the power applied to it. Power equals heat. More power, in you case, nearly three times the power I am familiar with, will result in the gearbox getting hotter.
Now for shorter periods of time and relatively low power, like my track day sessions where 30 mins is a long one and I have 300hp at the wheels, the oil seams to remain within reasonable limits. I have seen a max of 170F, very hot day and a long run of 25 mins. BUT and this is a BIG but the harder you run it, well... we are back to, more power over a longer period of time will result in heat buildup in the GB oil. Anyway really short periods like one good blast away from a streetlight shouldn't effect GB oil temp. If you can't reject the heat then long runs at high power outputs will continue to heat the oil until it fails. When the oil fails the gears won't last more than a few seconds.
And that's the real issue. As the oil heats up it will get to a point where is burns. I would get real concerned if the GB oil got any hotter than 190F degrees. (somebody who really knows chime in right here).
Some things to consider are oil type, limited slips, very high grip tires (slicks), and airflow over the GB itself among others. As far as limited slips go the ones that have a friction system will generate the most heat (alot) and the Quaife types quite a lot less. Also spinning the tires will heat things up real quick.
I intend to install a temp sensor and gauge in the G50 I have and go from there. If I see temp much above 170F I ma going to put a cooler in it with a pump and return the oil to 5th gear and the R&P. My box is already plumbed for this.
YOU however are in a place far beyond my planned 450HP. I would install a temp sensor and gauge and watch it very closely. You might need a pump no matter what you do. I would call a couple of GB vendors and ask your questions.
Don't save the few hundred it would take to put a cooler on it and FU a expensive GB. I don't know what you are thinking for a GB but forget anything cheap at those power levels. A Audi for example should last as long as the right foot can get to the floor the first time. You will find you are talking in the range of $15K to put together a power train to properly suit that much power.
You should ask this question on the GB page. You will get a lot of really good information.