  We have performed temperature dependent tunneling spectroscopy on an
impurity-free surface area of a LiFeAs single crystal. Our data reveal a highly
unusual temperature evolution of superconductivity: at $T_c^*=18$~K a partial
superconducting gap opens, as is evidenced by subtle, yet clear features in the
tunneling spectra, i.e. particle-hole symmetric coherence peaks, and a dip-hump
structure which signals strong-coupling superconductivity. At $T_c=16$~K, these
features substantiate dramatically and become characteristic of full
superconductivity. Remarkably, this is accompanied by an almost jump-like
increase of the gap energy at $T_c$ to about 87\% of its low-temperature gap
value. The energy of the bosonic mode as measured by the distance between the
coherence peak and the higher-energy dip remains practically constant in the
whole temperature regime $T\leq T_c^*$. The comparison of these findings with
established experimental and theoretical results lead us to suggest that the
bosonic mode is not directly related to incommensurate spin fluctuations that
have previously been observed in inelastic neutron scattering.
