  We determine the most probable length of paths at finite temperatures, with a
preassigned end-to-end distance and a unit of energy assigned to every step on
a $D$-dimensional hypercubic lattice. The asymptotic form of the most probable
path-length shows a transition from the directed walk nature at low
temperatures to the random walk nature as the temperature is raised to a
critical value $T_c$. We find $T_c = 1/(\ln 2 + \ln D)$. Below $T_c$ the most
probable path-length shows a crossover from the random walk nature for small
end-to-end distance to the directed walk nature for large end-to-end distance;
the crossover length diverges as the temperature approaches $T_c$. For every
temperature above $T_c$ we find that there is a maximum end-to-end distance
beyond which a most probable path-length does not exist.
