We use UV and extreme-UV emission lines observed in quiet regions on the solar disk with the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) instrument and the Extreme Ultraviolet Imaging Spectrometer (EIS) to determine the electron temperature in solar transition region plasmas. Prominent emission lines of O IV and O VI are present in the solar spectrum, and the measured intensity line ratios provide electron temperatures in the range of log T = 5.6-6.1. We find that the theoretical O IV and O VI ion formation temperatures are considerably lower than our derived temperatures. The line ratios expected from a plasma in ionization equilibrium are larger by a factor of about 2-5 than the measured line ratios. A careful cross-calibration of SUMER and EIS has been carried out, which excludes errors in the relative calibration of the two instruments. We checked for other instrumental and observational effects, as well as line blending, and can exclude them as a possible source of the discrepancy between theoretical and observed line ratios. Using a multi-thermal quiet-Sun differential emission measure changes the theoretical line ratio by up to 28% which is not sufficient as an explanation. We also explored additional excitation mechanisms. Photoexcitation from photospheric blackbody radiation, self-absorption, and recombination into excited levels cannot be a possible solution. Adding a second Maxwellian to simulate the presence of non-thermal, high-energy electrons in the plasma distribution of velocities also did not solve the discrepancy.