Surprisingly when I was looking this up, I figured out it was true. Due to recent research, the below was realised.
When we’re hot, we naturally cool our bodies primarily by sweating, or more specifically by having the sweat evaporate from our skin (that’s important!). Our bodies sense changes in tissue temperature by a network of thermosensors located in the skin and in more central parts of our body, which send input to our brain (specifically, the hypothalamus), which then initiates sweating.
When we take in a hot drink, it appears that the thermosensors located in the stomach become overactive, and send strong signals to our hypothalamus that we are hot. In turn, the hypothalamus reacts by initiating an over-compensatory sweating response. So, when this sweat evaporates from our skin, the heat energy we lose due to evaporation exceeds the heat energy gained by drinking the hot drink. In other words, it is because our body overacted to the hot drink that we end up cooler in the end