Does the body of the MOSFET consume current?
Let's look at an NMOS sideview:



Realize that an PN-junction is a diode. So there is a diode between Source (anode) and Body (cathode) and a second diode between Drain (anode) and Body (cathode).

For normal operation we want these diodes not to be in forward mode which means \$V_{sb}\$ and \$V_{db}\$ should not be negative (drain and/or source having a lower voltage than Body).

So your question is, what happens if we do violate that rule ?

Well then these diodes can operate in forward mode! What really happens as a consequence of that depends on the actual situation (circuit, voltages etc.). Fact is that while normally all current flowing through the NMOS will enter at the Drain and leave at the Source.

This will no longer be the case when one of the body diodes operates in forward mode. Part of the current will then "escape" via the body (substrate). That current will then follow a different current loop, the current is not lost nor is it "consumed". How much current that will be depends on many factors like, (forward) voltage across the diode, drain current, substrate doping level (that influences the resistance of the substrate).

The current through the substrate will cause a voltage drop and just like with every other diode, power will be dissipated. So yes, the body/substrate will heat up. By how much depends on the amount of power that is dissipated and what the thermal resistance to the outside world is.

You should realize that Drain-Body and Source-Body diodes behave just like any other diode so current will flow when in forward and power will be dissipated. These diodes do not have a "magic" property which makes them different from other diodes. Think about this: would it make sense for a diode not to conduct current when in forward mode or would it make sense that it does not dissipate power when clearly it is consuming power because there is a forward voltage and a current.