The limit is based on your radiators, how much "empty" sky you can point them at, and how hot you can get them. Those are all fairly finite. Space being vacuum, there's no particular "amount of heat" it can hold, when you radiate heat it just goes away. But there is a difference in bodies that can send heat to you.
In space, most of the environment is "cold" in that there's not much energy coming from it, so if you show the distant stars a hot radiator, it'll cool off pretty well, because it's all send and no receive. But nearby bodies are different: Earth is approximately room temperature (and in low Earth orbit takes up quite a bit of the sky); the Sun is pretty hot, for a much smaller portion of the sky (depending on your distance.)
If you're not near a planet, and you can reflect away most sunlight, you get pretty cold. See James Webb Space Telescope or anything else with sun shades, including the PSP.
The corona will change this a little, because it's a somewhat denser plasma than usual, but not by much. It'll still be a question of radiator size and heat, which is fairy easy to calculate.