No window? Listen for rain, wind, crickets, birds. If you're in a city, what sound do car tires make when they drive by? Sound like wet streets, or snow slush?
Maybe you could get some info on how much condensation forms on a glass of cold water. But that might just be measuring the inside temp.
Reminds me of the MIT question of how to find the height of a building with a barometer. The best answer was find the building superintendent and offer to trade the expensive barometer for the height of the building.
You might even be able to come up with a numerical guesstimate. Theoretically, a properly designed AC system is sized to run 100% of the time during the hottest weather. And obviously 0% if it's cool enough outside.
Or just look around the office and note how people are dressed, whether there are coats on people's chairs, how heavy those coats are, and whether you see any umbrellas lying around.
This is why, when I want to know what the weather is, I use the vast array of sensors that the US government has paid for, and the expertise of meteorologists. Just google it.