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It is due to thermal radiation. Bodies with temperature above absolute zero emits radiation. If frequency of the radiation is in the visual range the body "glows".

When the electrons in the atom are excited, for example by being heated, the additional energy pushes the electrons to higher energy orbits. When the electrons fall back down and leave the excited state, energy is re-emitted in the form of a photon. -wikipedia(emission spectrum)

This explains that heat itself is not giving off the light.

Spectral energy density as function of of wavelength and temperature

$u(\lambda,T) = \frac{8\pi hc}{\lambda^5} \frac{1}{e^{\frac{hc}{\lambda k T}}-1}$

If you integrate $u(\lambda,T)$ wrt $\lambda$ from $\lambda = 380nm$ to $\lambda = 750nm$ you will find that there is always some radiation in visual range. But it is very very small at room temperature(T = 300K) and hence undetectable to naked eye.

To get cut off temperature($T_c$) for glow. You need to solve

$\displaystyle \int_0^{T_c} \int_{\lambda = 380nm}^{\lambda=780nm} u(\lambda,T)d\lambda dT$ = minimum required to be detected by human eye.