I have a sony vaio laptop [model PCG K-23] that I bought 3 years back. Recently, I am facing a problem where my laptop automatically shutsdown after some time. Everyting seems ok but I don't know what is going on with the machine.

Does anyone know the resolution of the problem I am facing with my laptop?

Laptops shut down unexpectedly when there is a heat problem, expecially suspect in a 3 yr old laptop. Make sure that it hasn't lost its little feet underneath it so that there is a gap between the table and the bottom of the computer. Never use it on your 'lap', a bed, a tablecloth etc, which will prevent the cooling air flow.
Is the fan starting up? Sometimes the fan can be faulty and need replacing.
Is the heatsink clogged up with dust/hair/dirt etc. Sometimes you can clean the heat sink a little bit with a brush from the outside (make sure its turned off first), but a good clean really needs disassembling the computer to really get at it.