The finite-temperature binary collision method for treating spin-dimer systems: Taking TlCuCl3 as an example

► The bond-operator Hamiltonian for dimers above Hc is equivalent to a single-field one. ► The effective Hamiltonian for spin dimers can be identified as a renormalized one. ► Finite-T coupling is constructed by summing finite-T ladder diagrams. ► The effective Hamiltonian with finite-T coupling is better for hard-core systems at T>0.