  Black holes have been a subject of investigation over years not only because
they have interesting physical properties, but also because they seem to be the
appropriate tool for studying gravity in quantum scale. Although a lot of
effort has been made to understand the aspects of spacetime on the quantum
scale, the approach which includes noncommutativity of spacetime proves to be
promising among several possibilities. In this paper, we use the
Hamilton-Jacobi method to study the thermodynamic properties of cylindrical
black holes (black strings) in noncommutative spacetime. It is also
investigated the behavior of the black string in the presence of back reaction
as well as its influence on the system can be understood as an anomaly. This
work aims to provide understanding about black strings thermodynamics in
noncommutative spacetime since this scale of spacetime is important for the
comprehension of the relation between quantum mechanics and general relativity.
