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This may sound a little bit confusing, but I will try to explain. (I have done research on this topic already) I have looked at the temperatures of planets and I was wondering, is there a point where a planet is at perigee and it's temperature cannot reach any higher? Let's just say the planet is tidally locked, and is currently at perigee. Would the planet be at a point where it's temperature can no longer be increased at the current distance from its star?

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    $\begingroup$ By 'perigee' do you mean 'perihelion'? The terminology changes depending on what you're orbiting. $\endgroup$ – Phiteros Apr 12 '17 at 21:26
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    $\begingroup$ It has some, but not all to do with periapsis. Atmosphere retains heat, which makes a big difference. Look at Earth: with global climate change going the way it is, each new year has a hotter periapsis than the last. You can't generalize it based on orbital parameters because atmosphere size and composition matters. (Also to nitpick, perigee is only for orbits around Earth. Periapsis is the general form) $\endgroup$ – Cody Apr 12 '17 at 21:26
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    $\begingroup$ Wasp-12b is the hottest know planet, 1.5 jupiter masses at 1/44 earth sun distances from it's sun, it orbits once a day and is egg shaped. The so-called "tidal heating", and the proximity of the planet to its star, combine to bring the surface temperature to more than 2,500 K (2,200 °C). en.wikipedia.org/wiki/WASP-12b so the hotter it lives, the less it can last, lifespans shorter than 10mn years. $\endgroup$ – aliential Apr 13 '17 at 10:08
  • $\begingroup$ @Cody: I'm sure Venus would be an even better example... $\endgroup$ – AtmosphericPrisonEscape Apr 13 '17 at 12:13
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A planet in a stable orbit can only receive a finite maximum power from it's star and likewise can only generate a finite energy from internal heat (like our cooling core, which is a tiny power output compared to what we get from the Sun). There's a finite limit to available power.

If that power is not radiated out (which is thermal radiation) the planet's temperate would rise without limit. This never happens because hot things radiate heat (as EM radiation) to try and reach thermal equilibrium with their environment (which in the case of a planet is the very cold space around it).

So there must be a finite limit to the temperature any planet in a stable orbit can reach.

As @Cody indicated the actual point of maximum temperature may not be at periapsis.

Atmospheres can act in complex ways to raise the temperature of the surface significantly. Venus is a prime example as this page demonstrates. Without it's pressure cooker-like atmosphere we'd expect a temperature of around 240 K, whereas it's actually a rather staggering 740 K. But all of that is solar powered and can't rise without limit. But it illustrates the importance of atmospheric composition (and indeed the Greenhouse effect) on planets.

Update : I came across another page on the basic theory of planetary temperature while looking into something else. It may be of use so I've added it in this edit.

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