WOW you really do like going out on the edge.
Totally dependent on the atomic structure
http://www.dummies.com/how-to/content/the-process-of-natural-radioactive-decay.htmlThe electrostatic force is almost always significant, and, in the case of beta decay, the weak nuclear force is also involved.
PLEASE REMEMBER IN THESE DISCUSSIONS THE SPIN IS QUANTUM MOMENTUM DON'T MAKE IT CLASSICAL .. YET AGAIN
http://en.wikipedia.org/wiki/Weak_interaction 
Hot atom will live shorter ?
Electron period and temp ?
Electon period and motion >
e--C-----e -----------> c/2
e---C---e zero motion
No decay rate of atoms or electrons is unaffected by temperature but you can change the rates by playing around with the electrical structure in the correct way or by using the weak force.
In 1992 a group used good logic and created a shift of 0.9% in the decay rate of beryllium by firing specially prepared electrons at it.
can we desroy atom by hot/cold cycle faster ?
Nope the process is simply changing quantum spin and that process can be done repeatedly and as far as we know indefinitely.
can we destroy athome by cycles give photon / work
Not destroy you can excite them by sending in the right frequency photon and it will absorb the photon.
http://en.wikipedia.org/wiki/Absorption_(electromagnetic_radiation)
In physics, absorption of electromagnetic radiation is the way in which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed into internal energy of the absorber, for example thermal energy.[1] The reduction in intensity of a light wave propagating through a medium by absorption of a part of its photons is often called attenuation. Usually, the absorption of waves does not depend on their intensity (linear absorption), although in certain conditions (usually, in optics), the medium changes its transparency dependently on the intensity of waves going through, and saturable absorption (or nonlinear absorption) occurs.
can we evaluate efficiency
It is 100% efficient something you can't have in classic physics
I have seen lots of idiots try and claim it violates the 2nd law of thermodynamics .. it's a quantum effect and yes it violates the classic law and that's ok
how many photon enerrgy will be exchange to work ?
One
If you want to take it to the quantum extreme you can store that single photon inside the absorbing atom. The record for doing that scientifically stands at 60 seconds
http://www.extremetech.com/extreme/16228...-quantum-memory
how much time need athom for fotoemision how many energy will lost from single photon
Times of the exchange vary depending on atom but they are all very fast but you can't get an exact time.
That same old quantum problem all we can calculate is the probability to find the electron in a given state and the same for it's reaction with the photon.
So all you can do is use semi classical physics and mix in probabilities and what you get is a thing called Rabi frequency probability
http://en.wikipedia.org/wiki/Rabi_frequencySo if you pick a probability level you are happy with you get a time
The answer you really need to know however is fast very very fast.
A easy to understand guide to both processes is here
http://hyperphysics.phy-astr.gsu.edu/hbase/mod5.html
