The temperature dependence of the upper critical magnetic field (Hc2) in a BaFe1.84Co0.16As2 single crystal was determined via resistivity, for the inter-plane (H^ab) and in-plane (H//ab) directions in pulsed and static magnetic fields of up to 60 T. Suppressing superconductivity in a pulsed magnetic field at 3He temperatures permits us to construct an H-T phase diagram from quantitative Hc2(0) values and determine its behavior in low temperatures. Hc2(0) with H//ab (Hc2//(0)) and H^ab (Hc2^(0)) are ~ 55 T and 50 T respectively. These values are ~ 1.2 - 1.4 times larger than the weak-coupling Pauli paramagnetic limit (Hp = 1.84 Tc), indicating that enhanced paramagnetic limiting is essential and this superconductor is unconventional. While Hc2//ab is saturated at low temperature, Hc2 with H^ab (Hc2^) exhibits almost linear temperature dependence towards T = 0 K which results in reduced anisotropy of Hc2 in low temperature. The anisotropy of Hc2 was ~ 3.4 near Tc, and decreases rapidly with lower temperatures reaching ~ 1.1 at T = 0.7 K.