even if you are cooling the bulb, if you have it too close to your plants they will burn. about 12 inches clearance from the tops of the plants should be acceptable.
https://www.rollitup.org/indoor-growing/323608-my-first-grow-w-pics.html
That would depend on which of the wattage lights he went with, that if that was already decided and I missed it
ignore the rest. If he went with the 250-watt CoolTube with adequate light ventilation he could run that light right down just a tad off the plant tops.
When I used to grow with 250-watt lights I would try to keep them roughly 6 to 8 inches off the plant tops but 4 or less inches happened now and then and I seldom cooked anything and if I did it was minimal. A 250-watt does not put off all that much heat, yes way more than a CFL, but compared to higher wattage HID lighting, they run cool and even with a standard reflector you can run them pretty close.
You have to run them close because they only give off about 18 inches of decent light so if you hang it a foot over your plant tops you wasted one foot of your best light and only 8 inches, roughly, of your plant top is receiving decent light and the rest is in a low light situation.
You should not need a foot of space between a 400-watt CoolTube and the tops of your plants if the air movement to cool your light is adequate, but it would have to be a fair bit farther than a 250-watt light would .. and much closer to fitting what you said than a 250-watt light would be.
That is not meant in any way as an endorsement or suggestion to go with a 250-watt light.
I always say if you can use higher wattage, unless you are going into overkill, like trying to pull off a 1000-watt CoolTube in a computer case grow, pick the higher wattage. You do not have to go for it all but if you are trying to decide between a 150-watt light and a 250-watt light, pick the 250-watt light and if between a 250-watt light and a 400-watt, pick the 400-watt
and then if a 400-watt and a 600-watt .. again always pick the higher unless it is a case of overkill, you have more than surpassed you system needs to consistently supply a yield that always covers your needs.