Abstract We develop a method of synthetic frequency generation to construct an atomic clock with blackbody radiation (BBR) shift uncertainties below 10⁻¹⁹ at environmental conditions with a very low level of temperature control. The proposed method can be implemented for atoms and ions, which have two different clock transitions with frequencies ν ₁ and ν ₂ allowing to form a synthetic reference frequency ν _syn = (ν ₁ − ɛν ₂)/(1 − ɛ), which is absent in the spectrum of the involved atoms or ions. Calibration coefficient ɛ can be chosen such that the temperature dependence of the BBR shift for the synthetic frequency ν _syn has a local extremum at an arbitrary operating temperature T ₀. This leads to a weak sensitivity of BBR shift with respect to the temperature variations near operating temperature T ₀. As a specific example, the Yb⁺ ion is studied in detail, where the utilized optical clock transitions are of electric quadrupole (S → D) and octupole (S → F) type. In this case, temperature variations of ±7 K lead to BBR shift uncertainties of less than 10⁻¹⁹, showing the possibility to construct ultra-precise combined atomic clocks (including portable ones) without the use of cryogenic techniques.