Cooling by heating
Cooling a spacecraft by heating its radiators
A Spacecraft can only get rid of it's waste heat via radiative cooling. This is because there's practically no material surrounding it that could provide a path for conduction or convection that the waste heat could take.
For the purpose of radiative cooling bigger higher powered sattelites/spacecrafts need infrared radiators.
When the temperature of the radiators is kept constant then doubling the cooling power equates to doubling the area of the radiatiors. This furthermore roughly doubles the radiators mass (ignoring the mass of eventual fractal stiffening structures).
Since the radiated away power per unit area (areal cooling power density) scales with the fourth power of the radiators temperature (Stefan–Boltzmann law ) one can radiate away much more waste heat when the radiators are operated at a high temperature.
While possible today (TODO: check inhowfar that has been done)
actively pumping heat from the spacecraft into the radiators will be possible much more efficiently with diamondoid heat pump systems.
Of course the maximum temperature is limited by the thermal material degradation of the radiators. Some good refractory materials (those that don't contain rare elements) will become dirt cheap with advanced gem-gum technology.
Going to the ultimate limits requires rare elements though.
Going to the limits of spacecraft cooling
Warning! you are moving into more speculative areas. (level 1)
Instead of using refractory materials containing rare elements and still being not much more performant than with cheap refractory materials one could try the following: It might be possible to use a heat pump to dump the waste heat into a magnetically confined plasma that one slowly releases. A plasma at temperatures way above the melting point of all possible solid state materials and possibly even way above the temperature of the sun (just as in today's tokamak nuclear fusion experiments).
Possible problems are:
- plasma narrow band RF heating bottleneck (serious issue ...)
- plasma detachment from magnetic cage
This looks very much like the VASIMR (variable specific impulse magnetoplasmatic rocket) concept. So could it double as propulsion?
For cooling it's important to release a wide thermal energy spectrum carrying as much phase space away with it as possible. Narrowing the release angle should reduce phase space so double use for propulsion should degrade cooling capacity a bit.
The other way around, avoiding an undesired propulsion effect, may be an issue too.
Grazing the sun – A "mundane" form of star lifting
Warning! you are moving into more speculative areas. (level 3)
With this method: Could spacecrafts be sent near enough to the sun to replenish their released "cooling-plasma" (up to 200,000,000 K) with plasma from the suns atmosphere which is freezing cold in comparison (corona: 1,000,000 K)? This would likely mean dipping a bit into the (colder but denser) chromosphere (transition region).
- it may be hard to shield against deeply penetrating hard radiation spectral tails (X-ray to gamma)
- temperatures & densities:
corona temperatures > 1,000,000 K (very low density though!)
lower lying chromosphere: while temperatures are lower pressures are higher (effectively a higher thermal load?)
- at scooping depth atmospheric drag compensation likely becomes an issue
- extreme orbital speeds in periapsis significantly bigger than 100km/s
(TODO: check exact speeds and which temperature these corresponds to - these add to the environmental conditions)
note that extreme orbital speeds make scooping more efficient – crossing more volume per time
- likely negligible: interaction of magnetic systems of the spacecraft with suns magnetic field
Here's a density vs temperature chart of the Sun's atmosphere:  associated infos: 
Here's a density vs heigth chart for the Earth's atmosphere: 
80km ~ 2ng/ccm = 2mg/m³ ~ one orbit around earth => way too dense || 150km ~ 0.3pg/ccm = 0.3µg/m³ || 200km ~ orbiting earth about 24hours (about 16 orbits)
Since the sun is much bigger and massive than Earth one contacts much faster at much longer distance thus one will want to avoid dipping in as deep as in earths atmosphere.
(TODO: compare to galileo entry probe reentry conditions)
Related near term research is the Parker_Solar_Probe (Wikipedia). This probe will approach the sun as close as 8.5 solar radii. It is hoped that it will solve the mysterious origin of the high speed of the solar wind.
Note that 8.5 solar radii is nowhere near close enough to macroscopic amounts of gas. The original planned (but later cancelled) concept called for an approach as close as 3.0 solar radii. At this distance the sun already occupies an sizable chunk of the sky (solid angle). But this is still not at the point where the sun becomes a planar heat source occupying half of the "sky". At the point where the sun becomes a planar heat source further approach makes no difference in power density anymore. To hope for scooping up gas/plasma one absolutely has to go that deep.
Cooling whole Planets
Warning! you are moving into more speculative areas. (level 2)
With advanced gen-gum technology one could quickly start cooling down Venus by just reflecting back excessive in-falling light. The natural cooling process would take a very very long time though.
If one wants to speed up the cooling process significantly the cooling by heating method may be usable.
Also in a possible far off future where a one actually want's to use most of that energy and one taps a significant amount of it the cooling by heating method may be usable to prevent overheating of the whole planet.
A planetary cooling system would likely look like plants shining thermal light beams at temperatures between 2000K and 3000K away from the sun during nighttime / on the nightside of the planet.
If focusing does not degrade the cooling capacity too much (as explained further above) then part of the energy that's radiated away can be reused further out the solar system. This further degrades cooling efficiency though (due to receiver back-reflection).
In general this is about averting the "hypsithermal limit" and thus even applicable to earth.
Enabling magma submarines ?!
Warning! you are moving into more speculative areas. (level 3)
In case earth core probes turn out to be possible than the method of cooling by heating (solid state) radiators is of absolute essence. An unconditional requirement.
See main article "Deep drilling" for more speculations regarding this topic.
Easier accessible than the deep regions of terrestrial planets should be / may be the "deep" (still down only a tiny fraction of the planets radius) regions of gas giants. At these palaces one has a continuum in difficulty level with rising depth and a maybe less aggressive chemical environment (mostly hydrogen, helium and light non metal hydrides instead of iron and nickel).