Context. The prospects for using the asteroseismology of rapidly oscillating Ap (roAp) stars are hampered by the large uncertainty in fundamental stellar parameters. Results in the literature for the effective temperature (Teff) often span a range of 1000 K. Aims. Our goal is to reduce systematic errors and improve the Teff calibration of Ap stars based on new interferometric measurements. Methods. We obtained long-baseline interferometric observations of β CrB using the CHARA/FLUOR instrument. To disentangle the flux contributions of the two components of this binary star, we obtained VLT/NACO adaptive optics images. Results. We determined limb-darkened angular diameters of 0.699±0.017 mas for β CrB A (from interferometry) and 0.415±0.017 mas for β CrB B (from surface brightness-colour relations), corresponding to radii of 2.63±0.09 ${R}_\odot$ (3.4% uncertainty) and 1.56±0.07 ${R}_\odot$ (4.5%). The combined bolometric flux of the A+B components was determined from satellite UV data, spectrophotometry in the visible, and broadband data in the infrared. The flux from the B component constitutes 16±4% of the total flux and was determined by fitting an ATLAS9 model atmosphere to the broad-band NACO J and K magnitudes. By combining the flux of the A component with its measured angular diameter, we determined the effective temperature Teff  (A) = 7980±180 K (2.3%). Conclusions. Our new interferometric and imaging data enable nearly model-independent determination of the effective temperature of β CrB A. Including our recent study of α Cir, we now have direct Teff measurements of two of the brightest roAp stars, providing a strong benchmark for improved calibration of the Teff scale for Ap stars. This will support the use of potentially strong constraints imposed by asteroseismic studies of roAp stars.