We present new colour -- effective temperature (Teff) transformations based on the photometry of the early third data release (EDR3) of the Gaia/ESA mission. These relations are calibrated on a sample of about 600 dwarf and giant stars for which Teff have been previously determined with the InfraRed Flux Method from dereddened colours. The 1$sigma$ dispersion of the transformations is of 60-80 K for the pure Gaia colours BP-RP, BP-G , G-RP, improving to 40-60 K for colours including the 2MASS K-band, namely BP-K, RP-K and G-K, We validate these relations in the most challenging case of dense stellar fields, where the Gaia EDR3 photometry could be less reliable, providing guidance for a safe use of Gaia colours in crowded environments . We compare the Teff from the Gaia EDR3 colours with those obtained from standard V-K colours for stars in three Galactic globular clusters of different metallicity, namely NGC 104, NGC 6752 and NGC 7099. The agreement between the two estimates of Teff is excellent, with mean differences between -50 and +50 K, depending on the colour, and with 1$sigma$ dispersions around the mean Teff differences of 25-50 K for most of the colours and below 10 K for BP-K and G-K . This demonstrates that these colours are analogue to V-K , as Teff indicators.
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