We use high-quality VLT/UVES published data of the permitted O I triplet and Fe II lines to determine oxygen and iron abundances in unevolved (dwarfs, turnoff, subgiants) metal-poor halo stars. The calculations have been performed both in LTE and non-LTE (NLTE), employing effective temperatures obtained with the new infrared flux method (IRFM) temperature scale by Ramírez & Meléndez, and surface gravities from Hipparcos parallaxes and theoretical isochrones. A new list of accurate transition probabilities for Fe II lines, tied to the absolute scale defined by laboratory measurements, has been used. Interstellar absorption has been carefully taken into account by employing reddening maps, stellar energy distributions and Strömgren photometry. We find a plateau in the oxygen-to-iron ratio over more than 2 orders of magnitude in iron abundance (-3.2 < [Fe/H] < -0.7), with a mean [O/Fe] = 0.5 dex (σ = 0.1 dex), independent of metallicity, temperature, and surface gravity. The flat [O/Fe] ratio is mainly due to the use of adequate NLTE corrections and the new IRFM temperature scale, which, for metal-poor F/early G dwarfs is hotter than most T_(eff) scales used in previous studies of the O I triplet. According to the new IRFM T_(eff) scale, the temperatures of turnoff halo stars strongly depend on metallicity, a result that is in excellent qualitative and quantitative agreement with stellar evolution calculations, which predict that the T_(eff) of the turnoff at [Fe/H] = -3 is about 600-700 K higher than that at [Fe/H] = -1. Recent determinations of Hα temperatures in turnoff stars are in excellent relative agreement with the new IRFM T_(eff) scale in the metallicity range -2.7 < [Fe/H] < -1, with a zero-point difference of only 61 K.