Does thinking or focusing on something alter a neuron's speed? I Googled about this but couldn't find any thing precise to be that does thinking about something hard alters the speed of neurons impulses? I have heard of neurons velocity being variable but want to understand the exact circumstances in which the velocity varies.
There are, as far as I know, 2 main factors that determine the speed of action potential propagation:


Diameter: Axons with a large diameter have lower resistances, and hence higher conduction velocities;
Myelination: Myelin prevents passive diffusion of ions through the cell's membrane and increases charge separation across the cell membrane, speeding up conduction. Additionally, the spaces between the myelin sheaths, known as the nodes of Ranvier, facilitate saltatory conduction, which is akin to the action potential 'jumping' from node to node with a net increase in propagation as a consequence. 


These factors are physical properties of a neuron and hence are pretty much constant under physiological conditions, and are not influenced by thinking or focus.