For dislocation movement you don't need thermal barrier. What happens at elevated temperature is increased kinetic energy of atoms which helps in dislocation movement. But from pure theoretical point of view you can get dislocation movement also at 0K. What happens there is lack movement of other defects piles up dislocations much sooner to critical value. 

Books -

Freidel: ISBN  978-0080135236

Hirth and Lothe: ISBN 978-0894646171

See chapter 3 of the book "Mechanical Spectroscopy" of R. Schaller, G. Fantozzi, G. Gremaud, ISBN 0-87849-876-1

Dear Sir,

Thank you for your kind guidance, but unfortunately I could not find the book in library or in available internet resources. Can you please send me the copy on following address "[email protected]".

Best regards,

David, I hate to nitpick, but not only would there be no dislocation motion at 0 K, but there would be no movement of anything, atoms would not even vibrate. Additionally it is theoretically not possible to achieve 0 K. You can approach it, much like the speed of light, but never reach it. In the older open models of the universe this was called the heat death of the universe, although even a forever expanding universe would never cool to 0 K even if it continues to expand forever.

There is derivation about energy barrier in dislocation movement in "mechanical  behaviour of materials" book by T.H. Courtney. You can find answer of your question there.

Thank you