Special relativity predicts a very small influence of temperature on mass of around [Formula presented] ≈10^-14. More than 100 years ago, experiments were performed that revealed a limit of <10⁻⁸ for changes of a few degree at room temperature. A similar limit was obtained with a magnetic suspension balance at cryogenic temperatures. Recently, some measurements claim to have seen a negative dependence at the 10⁻⁶ level for a variety of metal samples at room temperature, which would be of interest e.g. to explain variations in the measurement of the gravitational constant. We have performed measurements with an analytical balance in vacuum and with a commercial thermogravimetric balance in argon and obtained a 3σ limit of <1.8×10^-8 for both metallic (Cu, Pt) and non-metallic (Al₂O₃) samples ranging from room temperature to above 1000 °C. This extends previous measurements to the high-temperature regime and rules out all claimed anomalies by more than two orders of magnitude.