Well, that is a very good question. TBH I don't know, since I've yet to set up my CMH (which would have the ballast remotely located). If I had to guess, I'd say about the same...but that's just a guess. One thing's for sure, the enclosed ballast on my 150w SunSystem hood does seem to generate quite a bit of heat (which is why I've already taken one apart, with the intention of using just the hood and socket assembly and modifying the hood to accommodate air-cooling). Maybe I should try first without the air-cooling modification? That would be a lot easier for me, since cutting the holes in the steel hood enclosure hasn't turned out to be all that easy.
When I lived in the northeast US, I found that the heat generated by the enclosed ballast actually helped keep the temps up during most of the year when outside temps weren't all that warm. It was only once in the summer (when I didn't have central AC) that my plants got a little stressed. However, now that I'm in socal, the temps don't get low enough for the enclosed-ballast to provide any real advantage, so I intend to move the ballasts out of both of my fixtures permanently. Maybe I'll try running one of 'em without poking any holes for air-cooling the fixture (and just cool the entire cab instead, with one fan+scrubber). I'm pretty sure that would work really well with the 150w lamp and a 2x2x4 cab, but I don't have a good feel yet for the heat generated by a 250w CMH bulb. Might be just fine. Supposedly, CMH bulbs run cooler than HPS, so a 250w CMH would seem to be a better option overall for a grow cab of this size.
I guess in the end, there' really only one way to find out, and that's to try it. It's actually pretty easy to move the ballasts out of these enclosed fixtures. I've spent a LOT more time trying to cut 'em down to a smaller size and adapt 'em for air-cooling. Probly coulda built a cool-tube set-up in less time. If you already have a 250w ballast that you plan to use, you could probly test it out by just disconnecting the internal (150w) ballast and rewiring the socket to the (remote) 250w ballast without actually removing the internal ballast. Then, if it turns out that the 250w bulb is too hot for your setup, you could just switch the wires back and keep using your 150w fixture until you can bump up your ventilation or whatever. Might be worth a try, since it would only involve removing a panel on the light fixture and doing a little re-wiring.