  We consider quantum computer architectures where interactions are mediated
between hot qubits that are not in their mechanical ground state. Such
situations occur, e.g., when not cooling ideally, or when moving ions or atoms
around. We introduce quantum gates between logically encoded systems that
consist of multiple physical ones and show how the encoding can be used to make
these gates resilient against such imperfections. We demonstrate that, in this
way, one can improve gate fidelities by enlarging the logical system, and
counteract the effect of unknown positions or position fluctuations of involved
particles. We consider both a classical treatment of positions in terms of
probability distributions, as well a quantum treatment using mechanical
eigenmodes. We analyze different settings including a cool logical system
mediating interactions between two hot systems, as well as two logical systems
consisting of hot physical systems whose positions fluctuate collectively or
individually. In all cases, we demonstrate a significant improvement of gate
fidelities, which provides a platform-independent tool to mitigate thermal
noise.
