why would my electrical cord on my rainbow vacuum cleaner become hot inuse ?

You do not say which end of the cord gets hot but I would guess the plug end...

The heat will be generated from a bad connection - probably in the plug - just a small amount of resistance in a bad connection where there's been a bit of sparking and blackening will cause heat to be generated.

Solution - cut off the plug and perhaps six inches of cord and fit a new plug.

If you leave it and allow it to continue to heat up then the insulation around the individual wires will eventually melt - they will touch together - fuses will blow and trips operate. The outer sheath may melt and cause a shock hazard.

Good Luck...
January 2016