  Resistive, magnetization, torque, specific heat and scanning tunneling
microscopy measurements are carried out on the hole heavily doped
CsFe$_2$As$_2$ single crystals. A characteristic temperature $T^*\sim13$ K,
which is several times higher than the superconducting transition temperature
$T_c=2.15$ K, is observed and possibly related to the superconducting
fluctuation or the pseudogap state. A diamagnetic signal detected by torque
measurements starts from the superconducting state, keeps finite and vanishes
gradually until a temperature near $T^*$. Temperature dependent resistivity and
specific heat also show kinks near $T^*$. An asymmetric gap-like feature with
the energy of 8.4 meV and a symmetric superconducting related gap of 2.2 meV on
the scanning tunneling spectra are detected, and these pseudogap-related
features disappear at temperatures up to at least 9 K. These observations by
different experimental tools suggest the possible existence of superconducting
fluctuation or pseudogap state in the temperature range up to 4 - 6 times of
$T_c$ in CsFe$_2$As$_2$.
