Context. The commonly used extinction laws of Cardelli et al. (1989, ApJ, 345, 245) have limitations that, among other issues, hamper the determination of the effective temperatures of O and early B stars from optical and near-infrared (NIR) photometry. Aims: We aim to develop a new family of extinction laws for 30 Doradus, check their general applicability within that region and elsewhere, and apply them to test the feasibility of using optical and NIR photometry to determine the effective temperature of OB stars. Methods: We use spectroscopy and NIR photometry from the VLT-FLAMES Tarantula Survey and optical photometry from HST/WFC3 of 30 Doradus and we analyze them with the software code CHORIZOS using different assumptions, such as the family of extinction laws. Results: We derive a new family of optical and NIR extinction laws for 30 Doradus and confirm its applicability to extinguished Galactic O-type systems. We conclude that by using the new extinction laws it is possible to measure the effective temperatures of OB stars with moderate uncertainties and only a small bias, at least up to E(4405 - 5495) ~ 1.5 mag. Appendices are available in electronic form at http://www.aanda.org