Clayers like it hot. We just need the heat to be inside the correct box.
Ice Point
This short essay touches on a lot of things, I will try and get it in a good linear organization.
Thermocouples work because metals exposed to differing temperatures in different places develop a voltage between those two places. Different metals produce differing voltages. So when you take say a chromel wire and an alumel wire and connect on end at the other end you will have a voltage dependent on the temperature at each end. These voltages are not linear. So if the meter end is at 70˚F and the connected end is at 170˚F you get a slightly different voltage than if cold end is at 75˚F and the hot end at 175˚F.
Further, if your two connections at your meter (you meter is almost certainly made with copper alloy wire) are at different temperatures you get two more thermocouples at the meter throwing off the measurement. Thermocouple wire, chosen to match the properties of the thermocouple usually connect the thermocouple to the meter (unless the thermocouple is directly connected).
The standard temperature for the end by the meter is 32˚F(0˚C), known in this context as the “ice point”. In order to get accurate readings you might have once placed this connection, watertight, in a bath of icewater. For years meters had electrical compensation for this temperature to make the meter read as if it were at zero. This was refered to as “ice point compensation”. Newer quality meters read the ambient temperature with a thermistor and compensate digitally. Cheaper meters assumed that they were at a particular temperature say 75˚F.
Old analog meters with a needle dealt with the non-linear aspect of thermocouples by printing a scale that was also not linear. Some parts of the scale had lines drawn closer together than other parts of the scale. It was a clever, inexpensive way to deal with the non-linearity.

Because of compensation, kiln control boards likely have on-board temperature sensing. Once they have that it is trivial to design a board to turn the kiln off if the ambient temperature is too high. In the US, having the means to turn off a malfunctioning kiln or kiln operating at an unsafe temperature is a liability issue. It also can vastly reduce kiln lifespan.

Derating of Electronics
Most electronics is designed to operate at or near room temperature. Cars use specific components that are vibration and heat resistant. The military and NASA have their own set of requirements. As you raise the ambient temperature the amount of current a device can take at one time and its lifespan falls. Even if a device is rated at say 120˚F it may fail sooner if operated or stored that hot. It also might need a larger heat sink (piece of aluminum designed to dissapate the heat).
Every electronic and electrical component in the kiln has a temperature rating. Just like elements fired at a higher temperature, power cords, relays, outlets, and control boards are going to fail sooner if operated at a high temperature. Circuit breakers trip sooner in hot weather too. Further as things get hotter, corrosion speeds up.
***Entropy discussion fits here.

I do not know exactly at what temperature Skutt Control Boards give a high ambient temperature warning, but I expect that the boards themselves are already above 100˚F. Heat gets to the control board a lot of ways, but there is insulation blocking much of the radiated heat, openings for convection, and little washer like things between the red box and kiln shell. Still the red box does heat up and consequently so does the control board. You can place a small fan to blow through the control box, something like an old computer fan, not a box fan. You want to avoid fans blowing on the kiln case.
Things that can be done to limit the heat in a kiln room. Open it up, windows, doors, fans in doors. Fire at night (make sure that you do not sleep in a house with a firing kiln). Start early in the morning. Fire faster so that less heat gets out of the kiln before you are done. Fire so that the hot part of the firing is in the evening if the outside temp is greater than 100 during the day.
My insulated studio gets warm in the winter with 1000 watts of heat. Your kiln say drawing 40 amps at 240 volts is just under 10,000 watts. This is a lot of heat and your air conditioner might not want to keep up with it. Plan ahead.
Please do not hang out in very hot kiln rooms and drink enough water. But make sure, especially in hot environments that you monitor your kiln.