Even with the doors wide open the you have a dead air space (ceiling area). Your ac unit does not bring in fresh air. You need to exhaust that stale air. You need a fan also to create a breeze. Air cooled hood is a good start. But don't skip the exhaust fan. See examples below:
Suncourt 8" Inline Duct Fan Rated at 500 cfm (cubic feet per minute)Tried and true tools for the heating and cooling trade, wisely adapted for cooling grow light reflectors. An Inline Duct Fan is a reliable and cost effective way to keep temperature in the indoor garden under control. Use one fan per light or to increase the efficiency of an exhaust system. These economically priced fans have a lesser cfm (cubic feet per minute air exchange) than the high output CAN-FANS also available on this site. Perfect for air cooling a single lighting reflector or ventilating a small closet sized grow room.
8" Inline Fan
EasyCool 6 - 6" INLINE AIR COOLABLE Reflector EASYCOOL6The EasyCool6 is a mid-sized reflector with MAXIMUM performance. The EasyCool6 features built in 6 cooling flanges and an innovative hinged and gasketed tempered glass lens. The EasyCool6 hinged lens allows for simple and easy access to the lamp, and the airtight gasket completely seals the unit for maximum cooling capabilities and CO2 enrichment. The reflective insert is high efficiency 95% reflective textured aluminum. The heavy duty housing features sturdy steel construction and a durable white finish.
Fits cordset from High Yield Lighting, Sunlight Supply, HTGSUPPLY.com Grow Lights, GrowBright and Digital Greenhouse
Dimensions: 18 long, 15 wide, 7.5 deep