I agree that 95 is too high especially if you don't have the ability to measure temps accurately most affordable devices are 2ºF high or low. Due to that I personally would say 91 (89-93 depending on the device)
The problem you have is that the enclosure has a huge heat loss. So first question what is it sitting on? What is the room temperature? Is there drafts in the room?
I'd try bundling a blanket around the sides of the container to try to hold a bit more heat in. Or try a folded towel on the lid. Add one not both and check the temps every 30 min until they stabilize with out a thermostat it can get out of control very quickly. If after they stop changing (usually a couple of hours) add the other either top or sides. Make sure the container isn't sitting on a cold floor or something that will sap heat like nothing else.