All books say only a single photon can remove an electron at a time. But we see that during thermal emissions electrons are removed by heat waves which are actually infrared rays. These infrared rays or photons increase the work potential of matter by increasing its temperature, so that even an infrared photon can release electron. Then must not we say that multiple photons can remove electron?
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All books say only a single photon can remove an electron at a time
That's probably a misstatement. A single photon can remove an electron, but that's not the only way that an electron can escape. The word "only" is the problem.
There are two different phenomena going on here.
When an object gets warm, the electrons in the material also heat up. You can think of the electrons in a metal as the atoms in a gas - they bump into each other, and all have different velocities as given by the Boltzmann distribution. When the material gets hot enough, some electrons will have so much energy that they can escape. That's a "bulk" property - not a direct result of radiation impinging on the material, but a result of the material heating up. You might say that many millions of photons contribute to the emission, because they contributed to the heating of the target. But that's not what we call the photoelectric effect.
In the photoelectric effect, a single photon can interact with a single electron and give it sufficient energy to escape. You can think of this as "heating up" a single electron to a very high apparent temperature - and it escapes before it has shared that energy with other electrons.
The effect is definitely real - you will see photo-emission for photons with sufficient energy (short enough wavelength, corresponding to the energy needed for electrons to escape) and it will exist regardless of the intensity of the radiation - in other words, it doesn't require you to heat up the cathode in order to see the emission. Einstein got his Nobel prize for figuring this out.
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Thermal emission is really a different process, driven by phonons not photons. Phonons are the vibrations of the crystal lattice itself. But more specifically, an intense coherent infrared light source like a laser can be used to eject electrons. See for example: http://www-ssrl.slac.stanford.edu/spear3/documents/schmerge_multiphoton_emission.pdf
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$\begingroup$ Good point about multi-photon interaction. I didn't think that's what the question was about - but you may be right. $\endgroup$– FlorisCommented Jan 18, 2016 at 17:38
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$\begingroup$ But even phoyons require photon as energy source. In photo electric effect a photon is given with such phoyon energy that electron escapes out vibrating. $\endgroup$ Commented Jan 18, 2016 at 17:48