Large stellar surveys of the Milky Way require validation with reference to a set of benchmark stars whose fundamental properties are well-determined. For metal-poor benchmark stars, disagreement between spectroscopic and interferometric effective temperatures has called the reliability of the temperature scale into question. We present new interferometric measurements of three metal-poor benchmark stars, HD 140283, HD 122563, and HD 103095, from which we determine their effective temperatures. The angular sizes of all the stars were determined from observations with the PAVO beam combiner at visible wavelengths at the CHARA array, with additional observations of HD 103095 made with the VEGA instrument, also at the CHARA array. Together with photometrically derived bolometric fluxes, the angular diameters give a direct measurement of the effective temperature. For HD 140283 we find {theta}_LD = 0.324+/-0.005 mas, Teff = 5787+/-48 K; for HD 122563, {theta}_LD = 0.926+/-0.011 mas, Teff = 4636+/-37 K; and for HD 103095 {theta}_LD = 0.595+/-0.007 mas, Teff = 5140+/-49 K. Our temperatures for HD 140283 and HD 103095 are hotter than the previous interferometric measurements by 253 K and 322 K, respectively. We find good agreement between our temperatures and recent spectroscopic and photometric estimates. We conclude some previous interferometric measurements have been affected by systematic uncertainties larger than their quoted errors.