Vintage Appliance Cords Getting Hot
Yes, normal and you should exercise all and extreme care when using vintage electrical appliances that generate heat. Many of these appliances would never pass modern UL or other saftey guidelines, and or would probably land their makers in court over injury lawsuits.
In order to replace the cord (which you should do by the way), you need to know the spacing of the prongs. Take the cord to any good hardware store, though you may have to search out one that has been around awhile, to find a certain match.
Other than the above, you can search eBay for "Roaster" or "vintage appliance" cords. There are several flavors, roaster, irons, coffee makers, etc, so again make sure what you are getting will fit your particular roaster.
Another thing:
Do *not* use oven cleaners, Comet or other types of cleansers, SOS/steel wool pads on aluminum cookware. It will damage the finish and hasten the breaking down of the finish.
WearEver (one of the largest makers of aluminum cookware and appliances), used to make a special cleaner for such things, but don't know if it is still sold/made. Cameo does have a cleaning powder for aluminum however. Other than these two there are various methods of cleaning aluminum using tartic acid or other substances. A quick "Googling" of "cleaning aluminum" should get you where you need to go.
Finally these vintage electric roasters, like many other portable ovens, hot plates and so forth from the time use quite allot of power. To be safe plug your roaster into an outlet (I prefer 20amp, but suppose 15 will do), with nothing else going at the same time on that line. As for the indicator light, it may be going from bright to dim as the heating coils cycle on and off. Again these babies take up allot of juice (just watch your electric meter spin when the thing starts heating),and depending upon internal wiring, the unit may direct as much power as possible to heating, even at the expense of the light.