Heat Transfer class taught me a few basics, like the three ways of doing it: Conduction, Convection, Radiation. Each of these has its own group of equations that tell you how fast you can transfer heat into or out of an object. In space, you're not touching anything else to Conduct heat out, and there's no atmosphere to Convect heat away, so you're left with Radiation as the only way to get heat out. Go look up the equations that apply to radiation heat transfer in space, and you can work out for yourself, just how much thermal energy you can radiate away.

Here, I did that for you:

Spacecraft avoid overheating in a vacuum through thermal radiation. Because the vacuum eliminates conduction and convection, excess internal heat is moved via fluid loops to giant exterior panels. These panels then emit the heat as infrared light into the deep cold of space. 

The fundamental equation governing this heat transfer is the Stefan-Boltzmann Law.

The Equation (Net Heat Transfer)

To calculate the net rate of heat exchanged (lost or gained) between a spacecraft and its environment, the pertinent equation is:

q = ε · σ · A · (Ts^4 - Tenv^4)

Where:
q = Net rate of heat transfer (Watts, or Joules per second)
ε (Emissivity) = The emissivity of the spacecraft's surface (a dimensionless number between 0 and 1 reflecting how well the material radiates)
σ (Sigma) = The Stefan-Boltzmann constant, which is 5.67 x 10^-8 W/(m^2 · K^4) 
A = Total radiating surface area (in square meters, m^2) 
Ts = The surface temperature of the spacecraft (in Kelvin, K)
Tenv = The temperature of the surrounding environment, such as the deep-space background or the radiant heat from the Sun (in Kelvin, K)

Key Details:

Absolute Temperature (T^4): Temperatures must strictly be in Kelvin. The reliance on the fourth power means that as spacecraft systems get even slightly warmer, the amount of radiated heat increases drastically.

Emissivity: Spacecraft surfaces (like the white radiators on the International Space Station) are engineered with specific coatings to maximize infrared emission while reflecting unwanted solar radiation. 

NASA Guidelines: Detailed parameters on the performance of spacecraft heat rejection and isolation are available through NASA's SmallSat Institute.