How long after the Big Bang would CMB radiation have been between 273 and 373 K? Cosmic microwave background radiation is 2.7 K today. When would it have been between 0 and 100 C?
The temperature of the cosmic microwave background scales as the inverse of the cosmic scale factor $a$. i.e. When everything was at half the separation it is now, then the CMB was twice the (absolute) temperature. The scale factor in turn is reciprocally related to the redshift by $a/a_0 = (1 +z)^{-1}$, where $z$ is the redshift and $a_0$ is the present-day scale factor, usually taken to be 1.

From this we see that
$$T(z) = T_0 (1+z),$$
where $T(z)$ is the temperature at redshift $z$ at some time in the past and  $T_0 = 2.73$K is the temperature of the CMB now. For the range of temperatures you specify requires redshifts in the range $99&lt; z&lt; 136$. 

Getting from a redshift to a time in the universe since the big bang is not so simple. The answer depends on what you take to be the "cosmological parameters" - i.e. the values of the cosmic matter density, the dark energy density and so on.

However, we can avoid looking "under the hood" and use a cosmology calculator. The one I have linked to is for a "flat" universe and has default values for what are currently good estimates for the matter density and present-day Hubble parameter. For the range of $z$ I found above, this corresponds to an age of between 10.8 and 17.3 million years after the big bang.

I guess you are perhaps thinking about these ideas that life could have been around about 15 million years after the big bang.