This paper is about the reasons of why the well known Fouriers Law of heat conduction is inconsistent with one of the main results of Einsteins theory of relativity, namely that the greatest known speed is that of the electromagnetic waves propagation in vacuum. Simple (but on solid physical arguments constructed) modifications to the laws of heat conduction will be presented that help to overcome this apparent paradox. Some of their fields of applications will be also presented with the aim to introduce teachers and students dealing with heat transfer problems to these questions that are not often discussed in standard text books and courses.