Here's a quick and dirty approximation:
Approximate a human with a water-sphere of radius $r$. Assume that blood circulation keeps the body temperature homogenous and that the skin keeps the water from boiling off (this isn't realistic but I figured this was the kind of situation you were thinking of). If we assume the sphere is a perfect blackbody, the heat loss due to thermal radiation is given by the <PERSON>-Boltzmann law:
$$ P_r=\sigma T^4\cdot A=\sigma T^4\cdot 4\pi r^2 $$
where $T$ is the temperature of the water and $A$ is the surface area of the sphere. The rate of temperature change will be:
$$ \frac{dT}{dt}=-\frac{P_r}{mC}=-\frac{P_r}{\rho VC}=-\frac{3P_r}{4\pi r^3\rho C}=-\frac{3\cdot\sigma T^4\cdot 4\pi r^2}{4\pi r^3\rho C}=-\frac{3\sigma T^4}{r\rho C} $$
where $m$ is the mass of the sphere, $C$ is the specific heat capacity of water,$\rho$ is the density of water and $V$ is the volume of the sphere. 707
Hence, we get a differntial equation of the form:
$$ \frac{dT}{dt}=-\frac{3\sigma T^4}{r\rho C} $$
If we make the ansatz: $$ T(t)=a(t+b)^n $$
and put it into the above equation, we get:
$$ an(t+b)^{n-1}=-\frac{3\sigma a^4(t+b)^{4n}}{r\rho C} $$
which gives:
$$ n-1=4n\Rightarrow n=-\frac{1}{3} $$
and
$$ an=-\frac{3\sigma a^4}{r\rho C}\Rightarrow a=\left(-\frac{nr\rho C}{3\sigma}\right)^\frac{1}{3}=\left(\frac{r\rho C}{9\sigma}\right)^\frac{1}{3} $$
If we assume $r$ is 0.5 m, we get:
$$ a=\left(\frac{0.5\cdot 1000 \cdot 4200}{9\cdot 5.67\cdot 10^{-8}}\right)^\frac{1}{3}\approx 1.6\cdot 10^4 $$
Hence T will change as:
$$ T(t)=1.6\cdot 10^4(t+b)^{-\frac{1}{3}} $$
If we assume that the temperature at $t=0$ is $37$ degrees C, which is approximately $310 K$, you get:
$$ 310=1.6\cdot 10^4b^{-\frac{1}{3}}\Rightarrow b=\left(\frac{1.6\cdot 10^4}{310}\right)^3\approx 1.38\cdot 10^5 $$
which gives:
$$ T(t)=1.6\cdot 10^4(t+1.38\cdot 10^5)^{-\frac{1}{3}} $$
Here I have plotted the time evolution of the temperature according to this formula:
As you see, it takes approximately 65000 s (almost 18 hours) for the sphere to freeze. This is obviously something of a worst case scenario. I have not included the effect of heat produced by the human body, incoming (solar) radiation, less than perfect emissitivty, possible insulation, etc. These could make it take much longer or even prevent cooling, depending on the assumptions. 374