Upcoming observations of the 21-cm signal from the epoch of reionization will soon provide the first direct detection of this era. This signal is influenced by many astrophysical effects, including long-range X-ray heating of the intergalactic gas. During the preceding cosmic dawn era, the impact of this heating on the 21-cm signal is particularly prominent, especially before spin temperature saturation. We present the largest volume (349 Mpc comoving = 244 h(-1) Mpc) full numerical radiative transfer simulations to date of this epoch which include the effects of helium and multifrequency heating, both with and without X-ray sources. We show that X-ray sources contribute significantly to early heating of the neutral intergalactic medium and, hence, to the corresponding 21-cm signal. The inclusion of hard, energetic radiation yields an earlier, extended transition from absorption to emission compared to the stellar-only case. The presence of X-ray sources decreases the absolute value of the mean 21-cm differential brightness temperature. These hard sources also significantly increase the 21-cm fluctuations compared to the common assumption of temperature saturation. The 21-cm differential brightness temperature power spectrum is initially boosted on large scales, before decreasing on all scales. Compared to the case of the cold, unheated intergalactic medium, the signal has lower rms fluctuations and increased non-Gaussianity, as measured by the skewness and kurtosis of the 21-cm probability distribution functions. Images of the 21-cm signal with resolution around 11 arcmin still show fluctuations well above the expected noise for deep integrations with the SKA1-Low, indicating that direct imaging of the X-ray heating epoch could be feasible.