Does your light fixture sit directly on your tank, possibly on a glass top? An enclosed air tight tank with a light fixture sitting on a glass top can heat up fast.
My light fixture is suspended and I have no glass top on my tank.
My 15G tank is in the corner of my kitchen surrounded by cabinets. Not the most ideal location when it comes to air circulation and heat dissipation. However, with a good fan, the tank has done great.
My house temp right now is 71 and the tank temp is 80-81 without a fan on.
In the summer time my house temp is kept high during the day (automatically steps up to 82 when no one is home) and the tank temp can go up to 86 with the fan running, but my corals and fish have been thriving. No sign of heat stress or I have not noticed it. My corals multiply fast and they maintain very nice colors all year round. As long as you can keep your tank temp from rising much higher than 86, you should be okay (at least from my experience.)
I think that the stability is more important than anything - no fast change, temp wise or water parameter wise.
I tried floating a frozen water bottle in the summer time in the sump of my 29G tank for a few days in a row (late afternoons when the temp was the highest.) The display tank did not look any different, but the sponges and pods in my sump/fuge were quite shocked to say the least.
Tomoko