Gravity and objects at 0K Let's say I put 2 objects at rest relative to each other with 0 Kelvin. Will they move towards each other because of gravity? Where they will get energy to move?
I don't have education in this field, just wondering.
 A: 
Will they move towards each other because of gravity? Where they will get energy to move?

Yes, they will move toward each other in the exact way that gravity ordinarily predicts.
The energy was there when you started.  Gravitational energy from the separation of two objects is a negative 1/r function.  This should confuse you if you've only now been introduced to the concept - it's a confusing concept.  We avoid this by encouraging students to only look at the energy difference between two different states.  Compared to a separation distance of $\infty$, all other separation distances have lower energy.
That means that these two objects will draw toward each other until they hit.  If they hit perfectly so that it doesn't eject any material, and they truly in-elastically combine, they will heat up.  That means the combination will no longer be very low temperature.  The system has converted gravitational energy into thermal energy.  This is why the universe "clumps" - the gravitational energy is lower entropy than the form of energy it is converted into (heat, radiation).
In the Newtonian sense, they can release infinite energy by getting infinitely close.  Of course, if you include knowledge of atomic physics, then obviously the objects can't be infinitely small.
Practically, large amounts of heating from gravitational collapse is common and very significant.  Large gas planets which are not large enough for internal fusion will heat themselves due to collapsing from gravity.  This releases energy, and can not be reversed without some external intervention.  Unsurprisingly, it is an entropy-increasing process.
The ultimate limit is forming a black hole.  Before matter gets to that point, a significant fraction of $m c^2$ (relative to its rest mass) of energy is liberated.  In other words, there is a lot of heat introduced, which was previously stored as gravitational energy.  The heating is so much that it creates x-rays and contributes to the bottleneck of a black hole swallowing matter.
Unless you've studied this a long time, this should all be quite counter-intuitive.  You just have to keep thinking and reading more until it makes sense.
A: Temperature is only well defined for systems of many particles, so you can't treat two masses using termperature (while of course the objects have a well defined Temperature due to thier composition of many atoms). Thus you can not really discribe the movement of two masses in term of their temperature.
Furthermore, no energy is needed for them to move to one another. This concept is known under potential energy, so just by the presence of the other mass they have some kind of energy (also called the configuration energy). Looking at it this way the configuration energy is just converted into "movement engery" (called kinetic energy).
I hope this answers your question, because I am not sure wether I understood it correctly. Otherwise, comment please.
A: Gravitation is only dependent upon rest mass and center-of-mass separation. It cannot be shielded or diverted.  Circumstances under which measureable footnotes appear are extreme.
Gravitation can self-cancel (internal to thin hollow homogeneous spherical shells).  It can be arbitrarily neutralized (local vacuum free fall).  Theory suggests to can be ruffled  by stellar-sized quadrupole moments (a pair of neutrons stars inspiraling and merging, Type IIa supernova core collapse).
Settle for an epsilon above 0 K.  You can be above 0 K (look around), you can be below 0 K (running lasers, MRI imaging), but you cannot be at 0 K.  Bad thing.  We can attain 100 picokelvins for diddling Bose-Einstein condensations.  We can also cool a body to its quantum ground state. 0 K is deeply forbidden for fundamental reasons.
