Presently, absolute radiometry is the main method of thermodynamic temperature determination above the silver point. The importance of such measurements has increased, as a large international project is underway aimed at assigning thermodynamic temperatures to high-temperature fixed points (HTFPs). All participants are using filter radiometers calibrated against an absolute cryogenic radiometer which, therefore, will be the basis of the provided thermodynamic temperatures of the fixed points. However, such a unified approach may lead to systematic errors (if any) common to all participants. There are methods, providing an alternative to absolute radiometry, which allow the determination of blackbody thermodynamic temperatures using relative measurements. Alternative methods, even if they have lower accuracy than absolute radiometry, could disclose some possible unrecognized systematic errors, or, on the contrary, could confirm the results obtained using absolute radiometry and increase confidence of the thermodynamic temperature determination. One such method, known as the method of ratios (i.e., double wavelength technique), is based on measuring the ratios of fluxes emitted by a blackbody in separate spectral ranges at two temperatures. This approach has been developed at VNIIOFI, but its realization met serious technical difficulties. Modern sensors with improved sensitivity and stability, extremely reproducible HTFP blackbodies, and significant progress in computational methods and computer performance provide a new chance to realize this approach with sufficient accuracy. Another method is based on comparing the ratio of fluxes 123 Int J Thermophys (2015) 36:252-266 253 measured at two wavelengths for a high-temperature blackbody with that measured for synchrotron radiation. This article overviews possibilities of the alternative methods for determination of blackbody thermodynamic temperatures by means of relative radiometry to attract attention of the thermometry and radiometry communities to the importance of international cooperation for realization of these methods.