1. The temperature difference is large: The greater the temperature difference between two objects, the faster heat will flow from the hotter object to the colder object. This is because a larger temperature difference creates a steeper thermal gradient, leading to a faster rate of heat transfer.

2. The materials have high thermal conductivity: Thermal conductivity is a measure of how well a material conducts heat. Materials with high thermal conductivity, like metals, transfer heat quickly, while materials with low thermal conductivity, like insulators, transfer heat slowly.

3. The contact area is large: The larger the surface area in contact between two objects, the more heat can be transferred. This is why a thick pan will heat up more slowly than a thin pan, even if both are made of the same material.

4. The materials are in direct contact: Heat transfer through conduction requires direct contact between the objects. The closer the objects are, the faster the heat transfer will occur.

5. The materials are thin: Thin materials allow for quicker heat transfer as the heat has a shorter distance to travel.

In summary:

* High temperature difference

* High thermal conductivity materials

* Large contact area

* Direct contact

* Thin materials

These factors all contribute to faster thermal conduction.