250w hps question

This is probably a dumb question but would a 250w hps be too hot for a 48"x48"x76" grow tent without cool tube setup? If so does anyone have any suggestions on how to cheaply remove the excess heat. Muchous gracious amigos.

Cheaply, open the door. Properly, get a ventilation fan.

If I keep it closed with a 8 in fan blowing some of the air will it be fine?

if I am not mistaken, 48"x48" is more than 4'x4' you need much more than 250w HPS for this area, at least 600w or 1Kw if you plan to flower them. oh and you definitely need exhaust fan.

Without extracting the air, you will just be blowing hot air around the room. Also, you need to extract the stale air so that fresh, co2 laden air is drawn in. And yes. 250 will be ok for veg (get a MH conversion bulb) but you really need a 600 for flower in a 4x4.
You need a 6" fan, at least 400 cfm for that. Even just the 250 would need a 4" fan. You will also need a filter if stealth is an issue.
I'm running a stealth 250w 2x2 scrog grow at the moment with a 6" 425 cfm fan and I'm struggling but my ambient temperatures are high.