Space is a very low temperature environment, however it also has an extremely small number of particles per unit volume. This leads me to believe that, contrary to popular portrayals of heat loss in space, there would be very little heat loss due to conduction on a hypothetical spaceship in deep space. If you were put into space and provided with food, water, heat, and protected from the pressure would the spaceship cool due to head radiating away from the ship?
Answer
If you are out of the sunlight, the main source of cooling will be radiation. The amount of net heat you radiate away depends on the temperature of your skin $T_{skin}$ and the ambient temperature of the surrounding environment $T_{ambient}$:
$\frac{Q}{t} = e \sigma A (T^{4}_{skin}-T^{4}_{ambient})$
where
$Q$ = heat loss in Joules
$t$ = time in seconds
$e$ = emissivity of skin ($\approx$ 0.98 for human body)
$\sigma$ = Stefan-Boltzmann constant
$A$ = surface area of human body
Plug $T_{skin}$ and $T_{ambient}$ into this calculator and it will calculate the heat loss in Watts using the equation above. For human body temperature ($T_{skin}$ = 34 °C = 307 K) and room temperatue ($T_{ambient}$ = 23 °C = 296 K), the heat loss is 133 Watts. For human body temperature and outer space ($T_{ambient}$ = -270 °C = 3 K), the heat loss is nearly 1,000 Watts.
Assume a human is 70 kg of water. Since water's heat capacity is 4.18 J/gK, if the person emits 1,000 Watts for ten minutes, that is only enough to decrease its temperature by 2 K. To balance the heat radiation away from your body you would need to consume food at 1,000 Watts = 14 food Calories per minute.
One of these 50 Calorie cookies every 2-3 minutes would do the trick.
In other words, you are right that space is not as "cold" as it is made out to be. Yes the temperature is low-- but there is not enough matter out there to cool down anything quickly. A Thermos is able to keep coffee hot for long periods of time by taking advantage of exactly this phenomenon.
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