What mechanism at the microscopic level determines whether a system heats up or not? When placed in an ordinary or a microwave oven, a beaker of water heats up except during boiling (i.e., a phase change involving latent heat). Now, suppose a system absorbs energy in such a way that the electrons are excited to higher energy levels. Will this necessarily heat up the system? In other words, is heating caused by the electrons or atoms in an object being excited to higher energy levels? 
 A: On the case of a microwave oven the water molecules in the food are made to vibrate. Water molecules are tiny electric dipoles and these are made to vibrate more strongly. The molecules stay in the electronic ground state. 
A: The microwave photon energy level gives rotational kinetic energy to water molecules due to interaction of the electromagnetic field with the water dipole molecule. The rotational kinetic energy is subsequently randomized to increase the average translational kinetic energy of the molecules, increasing the temperature of the water molecules. The microwave energy levels are well below those needed to excite electrons to higher levels. 
A regular oven cooks with infrared electromagnetic energy. The photon energy level corresponds to molecular vibration. These energy levels are likewise too low for electron excitation.
Hope this helps
A: The heat contained in a system can be thought of as the total kinetic energy of a system. my2cts' answer is correct, but I'll add that if you excite an electron to a higher energy level, that will indeed cause heating in many cases (see for example FRET).
The friction between the water molecules and the rest of the system is what causes things to heat up in a microwave. In a conventional oven, it's a direct transfer of kinetic energy from hot air.
Homework question: would something heat up in a microwave if it didn't contain any water?
