  Unlike most quantum systems which rapidly become incoherent as temperature is
raised, strong correlations persist at elevated temperatures in $S=1/2$ dimer
magnets, as revealed by the unusual asymmetric lineshape of their excitations
at finite temperatures. Here we quantitatively explore and parameterize the
strongly correlated magnetic excitations at finite temperatures using the high
resolution inelastic neutron scattering on the model compound
BaCu$_2$V$_2$O$_8$ which we show to be an alternating
antiferromagnetic-ferromagnetic spin$-1/2$ chain. Comparison to state of the
art computational techniques shows excellent agreement over a wide temperature
range. Our findings hence demonstrate the possibility to quantitatively predict
coherent behavior at elevated temperatures in quantum magnets.
