That's not how it works. Two bodies are in thermal equilibrium if there's no heat transfer between them: that's the zeroth law of thermodynamics. If you're colder than 2.73K in deep space, you will absorb the heat from the Cosmic Microwave Background. If you're hotter, you will irradiate heat away. So it does have a temperature.

Does this mean that if Earth stays a fixed distance from the sun then its equilibrium temperature is fixed? I remember people saying things like that the albedo of the ice caps affected the Earth's temperature.