Why is a temperature gradient set up in a heated rod? Suppose a cylindrical rod is maintained at 100 degree Celsius and the other at 0 degree Celsius. My book says that after reaching "Steady State" the rod will have developed a constant temperature gradient all throughout the rod.
Why does the rod reach a steady state shouldn't the rod keep absorbing heat until it reaches 100 degrees.
Assume the curved portion of the rod is perfectly insulated.
 A: In your problem statement, you assert that the two ends of the bar are both maintained at their respective temperatures of 100C and 0C.  This means it is not possible for the cold end to heat up to 100C. 
A: Apply Fourier's equation of heat conduction (here in one dimension, $x$, only):
$$\frac{\partial T}{\partial t}=\alpha \frac{\partial^2 T}{\partial x^2}$$
For Steady State temperatures no longer time-evolve:
$$\frac{\partial T}{\partial t}=0 \Rightarrow \frac{\partial^2 T}{\partial x^2}=0$$
$$\frac{\partial^2 T}{\partial x^2}=0 \Rightarrow \frac{\mathrm{d}T}{\mathrm{d}x}=c_1$$
After integration we get: 
$$T=c_1x+c_2$$
Where $c_1$ and $c_2$ are integration constants, found with boundary conditions ($L$ is length of rod):
$$x=0 \to T=100 \to c_2=100$$
$$x=L \to T=0 \to 0=c_1L+100$$
$$\Rightarrow c_1=-\frac{100}{L}$$
$$\boxed {T(x)=100\Big(1-\frac{x}{L}\Big)}$$
This is true only for a perfectly insulated rod. The case of a rod losing convection heat to the environment can be found in the link.
A: I think you want a conceptual answer, so:
Heat flows into the end of the rod that's in contact with the 100C source, and flows out of the end that's in contact with the 0C sink.
Unless forced by a heat pump of some sort, heat can only flow from a warmer place to a cooler place.  The rod is passive (does not contain any heat pumps), so the heat can flow in the rod only if there is a temperature gradient.
A: You can use your same argument for the $0$ degrees Celsius. 
In other words, you state:

... shouldn't the rod keep absorbing heat until it reaches 100 degrees?

But you could just as easily say "Shouldn't the rod keep 'losing heat' until it reaches $0$ degrees?" You might find this statement subjectively a little more unreasonable than your statement, but hopefully it can then show you how your question also cannot be the case.
To show why you get a constant temperature gradient, the other answers here explain why this is.
