What would be the temperature on Earth if We had no moon or sun?

About absolute zero, -237 degrees C. 

The moon has nothing to do with temperature on earth. But the sun is our only source of heat. 

The effects of the moon does effect the oceans with high tide and low tide.  I would also suppose that it affects land masses in a similar way so there will be some friction as the moon pulls on the surface and the surface mantle is a thin layer.  Frictional heat like rubbing 2 hands together quickly.  Not a hell of a lot of heat.

Eliminate the sun and you eliminate orbital gravity so the earth flies off like a BORG space ship.  So we have to wait to hit another planet to generate some heat.. It will not be a good night.  DAY is gone so it is only night.

I would say you better store up a couple thousand cords of firewood and a semi truck load of extra long life batteries...and a stack of 1000 wholly knickers.

The minimum temperature of anything in the Milky Way is around 10 Kelvin, but the Earth has internal sources of heat due to radioactivity in the magma so it would take billions of years to cool down that much.  Cooling to around 50 Kelvin would happen pretty fast.

If there was no sun, the temperature on Earth would be close to that of outer space, about -270 Celsius.

The moon has very little effect on the temperature of the Earth.

-270 degrees C.

No Moon.   No change.

No Sun -  Ice Age Completely frozen over.

Well below Zero

Very interesting question.

Terrestrial heat flow, that is, heat flow from the interior of the earth, would continue because our radioactive elements have not been all used up.  It is estimated that this heat flow is 30 to 40 terawatts (10^12 watts).  Perhaps it would speed up if the surface were not being kept warm by sunshine etc.  But let's go with 30-40 TW, and see what temperature that dictates for the earth's surface, which would presumably get into some sort of equilibrium state where all of the 30-40 TW are radiated away.

Note that I = sigma*T^4, the Stefan-Boltzmann Law of radiation, where I is watts per m^2, and T is absolute temperature.  The "sigma" is the Stefan-Boltzmann constant, 5.67 x 10^(-8) W/(m^2 K^4).

The area of the earth's surface is 510 x 10^12 m^2, so the radiation would be only around (1/15) of a watt per square meter!  Plug that into the SB Law and you get

(1/15) = 5.67 x 10^(-8) x T^4 =>

T^4 = 117.6 x 10^4 K =>

T = around 30 or 40 K ( = -230 or -240 degrees C).

So it would be "much" warmer than "outer space" (CMB at 3K) ... actually around the same as the surface temperature of our old friend Pluto is today.  But P would be much colder with no sun.

So... if Earth was simple adrift in space, not close to any other stars, it's own internal heat would keep the surface a *bit* warmer than the near-absolute zero of deep space, but not much...  and, with the surface so cold, the atmosphere would probably 'snow' down to the ground, adding to the crust's insulation between the surface and the mantle... I'd guess - 10 to 30 degrees Kelvin..?  There would still be hot spots - volcanic activity would heat *some* places on the surface, but for the most part - it's going to be very, very cold.

If it was above -100c (-148f) on the surface I’d be shocked, I’d say probably between -150c (-238f) and absolute zero (-273.15c/-459.67f)