  We report the first measurement of the temperature dependence of muon
transfer rate from $\mu$p atoms to oxygen between 100 and 300 K. Data were
obtained from the X-ray spectra of delayed events in gaseous target H$_2$/O$_2$
exposed to a muon beam. Based on the data, we determined the muon transfer
energy dependence up to 0.1 eV, showing an 8-fold increase in contrast with the
predictions of constant rate in the low energy limit. This work set constraints
on theoretical models of muon transfer, and is of fundamental importance for
the measurement of the hyperfine splitting of $\mu$p by the FAMU collaboration.
