Does the heat transfer rate depend on the temperature difference between the objects? . If I have a device that gets to temperatures of 2000-3000 F, and another object that's temp is 100-200 F Will the hotter object transfer the great faster since the other object is cooler and Since heat transfer to colder places. Or Will the heat transfer at the same rate?
 A: Short Answer:
The greater the temperature difference, the greater the rate at which heat transfers.
Longer more detailed answer, based on Wikipedia  Heat and Temperature
Heat is transferred by one or more of three processes.


*

*Conduction, an example of which is having the objects in physical contact.

*Convection, in which the heat is transferred though a medium, such as air, so it's a slower, much less efficient process.

*Radiation, which is how the heat of the Sun gets to us through the vacuum of space. 

The direction of heat transfer is from a region of high temperature to another region of lower temperature, and is governed by the Second Law of Thermodynamics. Heat transfer changes the internal energy of the systems from which and to which the energy is transferred. Heat transfer will occur in a direction that increases the entropy of the collection of systems.

One complication to the heat transfer process is Newton's Law of Cooling, although it does not apply to all three methods of heat transfer outlined above:
Newton's Law of Cooling

Newton's law of cooling states that the rate of heat loss of a body is proportional to the difference in temperatures between the body and its surroundings. As such, it is equivalent to a statement that the heat transfer coefficient, which mediates between heat losses and temperature differences, is a constant. This condition is generally true in thermal conduction (where it is guaranteed by Fourier's law), but it is often only approximately true in conditions of convective heat transfer, where a number of physical processes make effective heat transfer coefficients somewhat dependent on temperature differences. Finally, in the case of heat transfer by thermal radiation, Newton's law of cooling is not true.

A: The amount of heat leaving the hot object will be equal to the amount of heat received by the colder object (assuming nothing else is around to receive some of the heat).  The rate (in W) at which heat transfers from the hotter object to the colder object increases with the temperature difference between the objects.
A: The law of heat conduction, also known as Fourier's law, states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature.
A: As the temperature difference is bigger, the rate of temperature change will be bigger. The opposite is true as well.
A: One of the keys to remember is that the absolute law relates to two substances, each directly in contact with each other, and with no resistance to the flow of heat within them.  As a practical matter, no such substances exist; all substances present resistance to the flow of heat.  In the case of a radiator, for example, there is a thermal gradient within the internal fluid, within the metal separating the fluid from the cooling air, and within the air in contact with the metal; thus the two substances exchanging heat are not in direct contact.  The heat being removed from the fluid creates the internal gradient, because there is a resistance to the flow of heat within the fluid - just as there is within the air doing the cooling, while the metal separating the fluids also has a gradient across its cross sectional area.  All these make the transfer rate slower than the theoretical rate, and dependent on the resistance to the flow of heat within each of the substances involved in the transfer.
A: The rate of heat transfer between two surfaces is equal to the temperature difference divided by the total thermal resistance between two surfaces.
