Yes, unfortunately that's pretty hot.
You want to keep it under 70 degrees, preferably even lower. The room temperature is one thing, but fermentation itself produces heat and makes the temperature inside even hotter than the room. In a warm room, it's possible that the temperature of the fermenting beer is 8-10 degrees higher than the room. So, in a 75 degree closet, you can easily have an explosive 85 degree fermentation. The hotter it gets, the more likely it is to be explosive.
What I do is have an Igloo Icecube cooler that I put water in around the fermenter. I add a frozen water bottle or two as needed. I float a thermometer in the water, to check on the temperature. By doing that, I can easily keep the beer 10 degrees cooler than the room. I even made a new lid for my cooler, since the original one was hollow. That way, I can put the original lid back on when I want to use the cooler as, well, a cooler!
Here's a picture of my set up: