Howdy @M_Jake, welcome to Overgrow! With an air cooled lamp or proper exhaust and air movement a 400 watt setup should be able to dial into within a few degrees of ambient temperatures.
What is the current ambient temperature of your intake air?
It sounds like the heat from your lamp isn’t being adequately removed. Where does the exhaust go? Is it being removed fully or mixing back in with the intake air supply? If you don’t have an air cooled reflector directly at the lamps then you can basically view your entire space as the air cooled reflector that you are exhausting.
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Temperature is important. The best balance will be when temps are in order. Before the plants can utilize the energy from the lamps they must first be comfortable. It would be better to have the temperature in order than the lighting intensity maxed out. You can always let the plants grow into the lights, reaching up for it as they seek more energy. It may be more ideal to keep the lamps lower by until the temperatures correspond with comfortable levels for the plants that light and it’s inherent won’t be fully utilized. Temperature is a regulator of metabolism and metabolic activity.
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This depends on the genetics of the plant. An ideal situation may have the lighting from a 400 watt HID as close as 5 or 6 inches from the top of a canopy but that doesn’t mean one couldn’t have a successful harvest with lamps double or triple that distance from the canopy. Ideally have the lamps as close to the canopy as possible as long as they aren’t showing signs of stress from heat or light intensity. Too far away isn’t a specific distance, but rather a distance where the end product is unfavorable to you. Some stuff can produce full dense flowers with low levels of lighting intensity while other plants get super whispy and scraggy. It all sort of depends as these variables start to converge, temperature, relative humidities, lighting quality, and genetics.
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Are you not currently exhausting 24/7? It seems like they should be happening if you’re battling high temperatures. Additionally, as mentioned by @MissinBissin, fans to help circulate and mix up the air in the gardening space can help in maintaining comfortable temperature levels.
What are the specs of the fan you’re currently using to exhaust and what is the total volume of the space you’re exhausting? What is the ambient temperature of your intake air?
Hope this is helpful for you. Many blessings and much love