Also you guys, a terminology thing, if anyone cares: "heat content" can be misleading. Often we talk about heat moving into or out of a system, and useful work being done on or by a system; things that exist in the system as a volume are usually referred to as internal energy in closed systems or enthalpy in open systems. But this understanding of heat is violated by ideas like "heat content of the ocean", which is probably better understood as "quantity of heat that has been input into the ocean". It's a subtle distinction but worth keeping in mind!
Don't write this so small, this is important and a good point!
I didn't want to be an offtopic dick!
But I'll continue anyway
heat and work "happen" at system boundaries - they are not thermodynamic properties of a system. They do not define the state of a thermodynamic system: this is done in general by temperature, density, pressure, entropy content, internal energy etc. When we talk about converting "heat to useful energy" this means transferring heat into a system boundary, something happens within that system in a process, and work is exerted by that system through its boundary. In this sense, the role of the heat is to induce a change in the properties of the system that allow us to extract work from it.
Example: coal-burning power plant. Coal is burnt (in what we call ideally a high-temperature reservoir), transferring heat into a working fluid, e.g. water. The effect of this heat
transfer is to increase the temperature and (most notably) enthalpy and some other properties of the water. The water turns to steam, more-or-less, and is then put through a turbine or set of turbines in an 'expansion' process (so called because its pressure drops as this is done), in which its enthalpy is reduced by the turbine action. In this process the fluid does work
on the turbine, which is 'spun up' by the action of the fluid: this is the useful energy which eventually comes through your power supply. The working fluid as it comes out of the turbine has a low enthalpy and temperature, and it is put through an evaporator to shed further energy that could not be harvested by the turbine. This excess energy leaves the fluid as heat
. More work
is then put into the fluid for various reasons, to bring it to a condition where heat
can be dumped into it again by the burning of coal, increasing its enthalpy and temperature, and the process repeats.