Temperature-dependent current-voltage (I-V) characteristics of a molecule, 1,4-benzenedimetfaanethiol, was measured for 30 K < T < 300 K by a method of contact made by the electrochemical deposition of a platinum electrode in a lateral configuration. The I-V characteristics are nonlinear and asymmetric in the entire temperature range and the current decreases with decreasing temperature down to 40 K. Below 40 K, the I-V characteristics become temperature independent. The asymmetric I-V characteristics can be understood as arising from a better contact on one side (made by the self-assembled monolayer) than on the other side (made by the electrochemically deposited Pt electrode). The activation energy of thermally activated conduction for T > 100 K is typically 0.11 eV. For T < 40 K, the observed temperature independent I-V characteristics are fitted to the Fowler-Nordheim tunneling expression with barrier height of 1-2 eV depending on the contact strength of samples.