To answer your question – no. It is the brain that ‘thinks’ and does complex cognitive reasoning. And actually, it depends what you mean by ‘thinking’. I have studied Neuroscience for a long time and there is no evidence to suggest that the type of complex reasoning you are talking about is performed by any organ other than the brain (in any animal).
It is true that other organs than the brain produce neurohormones, but it doesn’t mean these organs are the site of action of these neurohormones.
As for the specific parts of the brain involved – I don’t know – there is still a lot of research on this going on. The telencephalon is part of the brain, and includes both the cerebral cortex and sub-cortical regions. There is strong evidence to suggest the prefrontal cortex (cortex) and hippocampus (sub-cortical) are highly-involved in complex reasoning. And many other parts of the brain are also involved in conscious and unconscious cognitive processes.
Yes, we also have a brainstem, a spinal cord and an enteric nervous system, which perform complex neural computations – but they do not ‘think’ the way we commonly think about thinking. As for non-neural parts of an organism – there is no evidence that those ‘think’.
I hope this help. I'd be interested in what others have to say on this.
BSc (Biomedical Sciences – Neuroscience) (UCL)
Here are some references that I studied from last year:
These University-level textbooks:
--- "Anatomy and Physiology" by Tortora et al;
--- "Neuroscience" by Purves et al;
--- "Principles of Neural Science" by Kandel et al;
The Making of Memory by Steven Rose;
The Human Brain by Susan Greenfield;
From Neuron to Cognition via Computational Neuroscience
Cerebral cortex – Scholarpedia article
An integrative theory of prefrontal cortex function,
Miller & Cohen 2001, Annual review of neuroscience
The hippocampal system mediates logical reasoning about familiar spatial environments, Goel et al 2004 - Journal of Cognitive Neuroscience, MIT Press
Role of the hippocampus in imagination and future thinking
Maguire & D Hassabis - 2011 - PNAS
Think Twice: How the Gut's "Second Brain" Influences Mood and Well ...
may be useful:
As for evidence that anything else than networks of neurons can enable cognitive processes – eg. skin in your leg or bone in your arm – I have never seen. Although computer transistor circuits are a possible (non-biological) candidate.