Heat and work make me think of thermodynamics.
1) The first law of thermodynamics relates heat Q and work W to the variation of internal energy:
This law says that the internal energy of a body (the sum of ALL the energies, kinetic and potential, of all the particles of the body) can change only when you exchange heat or work with the body.
You can increase the internal energy of a metal block by lighting a fire underneath (heat) or beating it with a hammer (work).
You can "see" the increase of internal energy because the temperature of the metal block (that is the macroscopic telltale of internal energy) increases.
A great example of this situation is the Joule's Experiment using the calorimeter and falling weight!!!!
2) The second law of thermodynamics also relates heat and work introducing the impossibility to convert completely heat into work using a heat machine, as in the next figure:
Consider a steam engine. It takes heat Q1 and converts some of it into work BUT it also releases part of the absorbed heat into the atmosphere (Q2)!!!
So, the efficiency will be always less than 1 (meaning that you cannot convert 100% of heat into work)!!!