Unless your room temperature is the same as a walk-in freezer, ice cubes are going to melt since they need to stay below freezing (32 degrees F) to stay in that form.

Because the melting point of ice is below room temperature.

same but opposite reason that water freezes. The most common phase transition to ice Ih occurs when liquid water is cooled below 0 °C (273.15 K, 32 °F) at standard atmospheric pressure.

Almost any substance will change state from a solid to a liquid when given enough energy to break the inter-molecular bonds between the individual atoms. There are 4 main inter-molecular forces and are all consequence of electron density around the molecules. In order of ascending strength: Vaan der Wall or London forces are the weakest and are caused by the constant variations in electron density. Where there is extra electron density on part of one molecule, the increased negative charge pushes electrons away from that area of the touching molecule. This in turn lets these electrons 'see' more of the nucleus from the next molecule and they are attracted. It is this reason the forces are also known as induced dipole-induced dipole forces. The next strongest are dipole-induced dipole forces. These come about by a molecule with a permanent dipole caused by two adjoining atoms with different electronegativities (too much to go into in this answer), induce a dipole in a neighbouring molecule hence causing an attraction similar to the effect above. Next are dipole-dipole interactions which are caused by two molecules with permanent dipoles such as two molecules of HCl. The strongest by far are hydrogen bonds which are present in abundance in water. These are caused when a hydrogen atom is directly bonded to an electronegative nitrogen, oxygen or flourine atom. The electronegative atom withdraws electrons from the hydrogen which in turn attracts electronegative atoms. This creates a massive networked structure which holds itself together. It isn't until enough heat energy is given to overcome these forces that the substance can change state. Water experiences all of these forces and so it has an unexpected high boiling point compared to similar molecules without these inter-molecular forces. I hope this helps.

cause it gets too hot for them

9-9-2017 When you observe something, that is science. When you ask why, that is religion. You are in the wrong category to be asking a religious question.

cause they get warmer probably

Ice cubes will melt whenever the ambient air temperature gets above 32 degrees.