Floor heat cables under linoleum flooring?
What you're referring to as Linoleum is probably vinyl.  At room temperature, it's fairly solid and the good stuff will bridge minor variations in the surface without it showing through.  By minor, I mean shallow embossed texture in the surface of the layer below, or thin grout lines between tiles.  Even at room temperature, heat ribbon is likely to eventually show through because the vinyl slowly conforms to the surface.  

When you warm it, the vinyl softens and becomes flexible and stretchy.  In fact, warming the vinyl is a trick for getting it to conform in a problem area during installation, or for getting vinyl planks to stay together when some irregularity underneath pushes them apart.  If you lay heat ribbon directly under the vinyl rather than embedding it in a smooth surface, the vinyl will conform around it and the ribbon will show on the surface.

If you don't want to embed the heat ribbon in another layer, you may be able to accomplish the result with radiant heating film.



There are a number of versions.  In general, it comes in rolls of fairly wide, thin, flat plastic film.  Sandwiched inside the film is a resistive layer.  You make the electrical connections at the wall and hide it with molding.

Doing this under the floor adds a lot of delay from the time you turn it on until the heat gets through the floor and starts warming the room.  An alternative with much faster heating is to use the film on the ceiling and paint over it to hide it.  The sensation of using it that way is a little like having a heat lamp in the ceiling; your head will feel a lot warmer than your feet.