  Successful implementation of thermal leptogenesis requires re-heat
temperatures T_R\agt 2\times 10^9 GeV, in apparent conflict with SUSY models
with TeV-scale gravitinos, which require much lower T_R in order to avoid Big
Bang Nucleosynthesis (BBN) constraints. We show that mixed axion/axino dark
matter can reconcile thermal leptogenesis with the gravitino problem in models
with m_{\tG}\agt 30 TeV, a rather high Peccei-Quinn breaking scale and an
initial mis-alignment angle \theta_i < 1. We calculate axion and axino dark
matter production from four sources, and impose BBN constraints on long-lived
gravitinos and neutralinos. Moreover, we discuss several SUSY models which
naturally have gravitino masses of the order of tens of TeV. We find a
reconciliation difficult in Yukawa-unified SUSY and in AMSB with a wino-like
lightest neutralino. However, T_R\sim 10^{10}-10^{12} GeV can easily be
achieved in effective SUSY and in models based on mixed moduli-anomaly
mediation. Consequences of this scenario include: 1. an LHC SUSY discovery
should be consistent with SUSY models with a large gravitino mass, 2. an
apparent neutralino relic abundance \Omega_{\tz_1}h^2\alt 1, 3. no WIMP direct
or indirect detection signals should be found, and 4. the axion mass should be
less than \sim 10^{-6} eV, somewhat below the conventional range which is
explored by microwave cavity axion detection experiments.
