Observations of cold O+ beams (COBs) in the lobe/mantle region of Earth's magnetotail showed that O+ ions originating from the ionosphere can stream into the distant tail (40--200 RE). These O+ ions have a high parallel streaming energy (~1--20 keV) and low perpendicular thermal energy (~70--210 eV) in the distant tail. In this paper, we propose that the nonadiabatic shock heating of O+ ions in the polar magnetosphere and the subsequent adiabatic evolution of ion velocity can lead to the occurrence of COBs in the tail lobe. The heating and acceleration of heavy O+ ions by fast shocks are studied by a theoretical analysis and hybrid simulations. It is found that after the passing of fast shock, heavy ions gain a gyration speed Vg $simeq$ MAVAsin($theta$2 - $theta$1)/cos$theta$1, where MA is the upstream Alfv¿n Mach number, VA is upstream Alfv¿n speed, and $theta$1 ($theta$2) is upstream (downstream) shock normal angle. After heating, the adiabatic evolution in the tail lobe can transfer a major part of perpendicular thermal energy T$perp$ to the observed parallel streaming energy W$parallel$. We have found that weak fast shocks in the polar magnetosphere with MA $simeq$ 1.05--1.2 can lead to the observed streaming energy associated with COBs. Weak fast shocks in the magnetosphere can be generated by the interaction of interplanetary shocks/discontinuities with Earth's magnetosphere. Escaping ionospheric O+ ions can gain enough energy from shock heating to account for observations of COBs in the tail lobe. For example, the ion heating by a shock with MA ~ 1.11at a radial distance of rs = 6.5 RE can lead to COBs with O+ streaming energy W$parallel$ ~ 5 keV and perpendicular thermal energy T$perp$ ~ 220 eV observed at x = 185 RE.