Conducting polymers are chain like aromatic/aliphatic in nature and hopping mechanism applied on it.
The conductivity of a material is generally dependent on the flow direction of the mobile charge carriers. If the material is isotropic, its mobility will be equal in all directions and a one dimensional model is sufficient. If the material is unisotropic it is also sufficient to determine the mobility in the the direction of interest.
A demonstartive example in the literature is poly crystalline columnar structure. In the directions of the columns the mobility is different from that in the perpendicular direction. Since one is interested in the conduction process in parallel to the columns,then the mobility is determined in this discretion. So if your organic material is oriented along the molecules for example, i think it is sufficient to pay attention to this direction. In pol-crystalline materials the the grain boundaries are the most effective in impeding the motion of the mobile carriers.
wish you success
Your question and the statement below
"Will Quasi-one-dimensional model explain the conductivity mechanism of conducting polymers in low temperature range?
Conducting polymers are chain like aromatic/aliphatic in nature and hopping mechanism applied on it."
is a typical old-fashioned and nevertheless wrong assumption. All the conductive polymers consist of more or less spherical nanoscopic primary particles (about 10 nm in size), the arrangement of the polymer chains is very complicated and has not been confirmed in detail (for no conductive polymer).
For Polyaniline, I was able to resolve the structure at least basically:
https://www.researchgate.net/publication/49593603_New_Insight_into_Organic_Metal_Polyaniline_Morphology_and_Structure
The conductivity mechanism can not be described by quasi-one-dimensional models, also not at low temperature, instead of this you have a 3-dimensional conductivity consisting of a contribution inside the primary particle (about 8 nm diameter) and from particle to particle (tunneling).
The mechanism inside the primary particle can be more like an insulator's conductivity or like a metal (for my polyaniline type, I was able to generate and analyse the "insulator-to-metal" transition which is not possible for all conductive polymers, but requires very special preconditions and processes).
For an overview, you can read this:
https://www.researchgate.net/publication/255785634_Metallic_Properties_of_Conductive_Polymers_due_to_Dispersion
https://www.researchgate.net/publication/253651172_Conductive_Polymers_as_Organic_Nanometals
Also you can find all kind of original papers in my RG site.
Article New Insight into Organic Metal Polyaniline Morphology and Structure
Chapter Metallic Properties of Conductive Polymers due to Dispersion
Chapter Conductive Polymers as Organic Nanometals
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