A lot will depend upon the surrounding temperature, but I think that 400W will do bad things the few times that you can't open the tent every 2 hours. I recently switched from a 400W (old) HPS to 300W LED because of heat.
I'm growing on my 2nd floor which doesn't get as good of AC as the main floor. The room will normally hit hit 27.5-29.5 C on warm days, and before when I was exhausting from the tent into the room, the room got to 32+C and the tent was 34C. Now I'm exhausting out the tent to the window (I cut a piece of solid foam insulation board (cheap) to fit my partially open window and cut a hole for the duct to go into), and the room's back to 27.5 and the tent is 28.5C.
Back when I used to grow in a basement, I ran my 400w HPS in a 4'x4'x4' rigid box I made (and wow was that 4' height a challenge!). Even in the basement in such a small space I needed to exhaust heat from the box. Exhausting heat into the rest of the basement was fine even during the summer. I was able to get a cheap (but loud) used bathroom fan to exhaust the box - maybe check your local classifieds. If nothing else, there are cheaper "duct fan"'s that will help, even if the amount of air flow won't be much, and they'll wear out faster than an inline will.