► ETo estimate with limited weather data may cause strong under and overestimations. ► Maps showing under and overestimations of ETo are presented for Mediterranean. ► FAO temperature based method for ETo estimate is recommended. ► A correction for aridity and humidity of sites could improve ETo estimate. ► Temperature based ETo methods should be calibrated for local conditions before use. The standard FAO Penman–Monteith (PM-ETo) method for computing the reference evapotranspiration (ETo), in addition to air temperature, needs data on solar radiation or sunshine duration, relative humidity and wind speed which are often lacking and/or do not respect appropriate quality requirements. Hence, in many cases, ETo has to be estimated with limited weather data using maximum and minimum temperature only. Essentially, two procedures are used when no more than temperature data are available: (i) the well-known Hargreaves–Samani equation (HS), or (ii) the PM-ETo method with weather parameters estimated from the limited available data, called PM temperature (PMT) method. The application of these temperature-based approaches often led to contradictory results for various climates and world regions. The data used in the analysis refer to 577 weather stations available through the CLIMWAT database. The results, confirmed by various statistical indicators, emphasized that: (a) in hyper-arid and arid zones, the performance of HS and PMT methods are similar, with root mean square errors (RMSEs) around 0.60–0.65mmd−1; (b) in semi-arid to humid climates, the PMT method produced better results than HS, with RMSE smaller than 0.52mmd−1; (c) the performance of PMT method could be improved when adopting the corrections for aridity/humidity in the estimation of the dew point temperature from minimum temperature data. The spatial elaboration of results indicated high variability of ETo estimates by different methods. Thus, a site-specific analysis using daily datasets of sufficient quality is needed for the validation and calibration of temperature methods for ETo estimate. Maps presenting indicative results on under/over estimation of ETo by both temperature methods may be useful for their more accurate application over different Mediterranean climates.