  Protein folding is a universal process, very fast and accurate, which works
consistently (as it should be) in a wide range of physiological conditions. The
present work is based on three premises, namely: ($i$) folding reaction is a
process with two consecutive and independent stages, namely the search
mechanism and the overall productive stabilization; ($ii$) the folding kinetics
results from a mechanism as fast as can be; and ($iii$) at nanoscale
dimensions, local thermal fluctuations may have important role on the folding
kinetics. Here the first stage of folding process (search mechanism) is focused
exclusively. The effects and consequences of local thermal fluctuations on the
configurational kinetics, treated here in the context of non extensive
statistical mechanics, is analyzed in detail through the dependence of the
characteristic time of folding ($\tau$) on the temperature $T$ and on the
nonextensive parameter $q$.The model used consists of effective residues
forming a chain of 27 beads, which occupy different sites of a $3-$D infinite
lattice, representing a single protein chain in solution. The configurational
evolution, treated by Monte Carlo simulation, is driven mainly by the change in
free energy of transfer between consecutive configurations. ...
