Air pressure will always flow from high pressure to low pressure. This is why a tornado shows up when there is a high pressure front moving into a low pressure front - with cold air and hot air respectively circling around and interacting with each other. It’s the same reason that hot air rises and cold air sinks.
As the air gets warmer, it gets lighter. As a balloon filled with helium, it rises. If the air gets cooler again, it sinks, like a balloon that has been filled with breath. If the air is moving between rooms, sometimes one can feel the change in air pressure. If that’s not possible because it’s not big enough, the change can usually be detected with a candle.
