The Earth's mantle is a layer of hot, dense rock that lies beneath the crust and above the outer core. Here's a breakdown of where you'd find the hottest and coolest parts:

Hottest Parts:

* Lower Mantle: The lower mantle is the deepest section of the mantle, extending from around 660 km to 2,900 km depth. It's subjected to immense pressure from the weight of the Earth above, and the heat from the Earth's core. Temperatures here are estimated to reach upwards of 3,700°C (6,700°F).

* Mantle Plumes: These are narrow columns of hot rock that rise from the lower mantle towards the surface. They often lead to volcanic activity on the Earth's surface. The rock within the plumes is significantly hotter than the surrounding mantle.

Coolest Parts:

* Lithosphere: The lithosphere is the rigid outermost layer of the Earth, composed of the crust and the uppermost part of the mantle. It's considered relatively cool compared to the deeper mantle.

* Subducting Plates: When tectonic plates collide, one plate can be forced underneath the other (subduction). This sinking plate, made of lithosphere, carries relatively cool material into the mantle.

Important Note: While we use terms like "hot" and "cool" to describe the mantle, we're dealing with extremely high temperatures that are far beyond what humans can experience. The coolest parts of the mantle are still incredibly hot, just comparatively cooler than the depths.