Yeah, routers can get warm, but excessive heat is a problem. They have a specific operating range.
First, check the environment. The operating temperature must be between 0°C and 40°C (32°F to 104°F). If the room is hotter than that, it will overheat. Move it away from direct sunlight, heaters, or other heat sources. Make sure all vents are clear and it's sitting on a flat, hard surface, not on a carpet or buried in a cabinet.
Also, keep it away from equipment that generates heat and interference, like microwaves, refrigerators, or heavy-duty motors.
IF THAT DIDN'T WORK: Confirm you're using the correct power adapter. An incorrect adapter with higher voltage can cause overheating and damage. The specs are +19V/2.37A or +19.5V/2.31A.
HEADS UP: If it's still excessively hot within the correct temperature range, the internal cooling might be failing. Persistent overheating will shorten its lifespan. Consider contacting ASUS support.