Did you get the ceramic type with the recessed resistor wire?
Yeah it's normal for them to get hot and you'll want to be sure Nothing that can melt or catch on fire comes in contact with it.
Last year I rewired my Uncles 41 Coupe to 12V and he came out with a box containing a full restored radio 6V so I installed it but had to wait to wire it up until I ordered a voltage reducer from Ron Francis. It also dropped the volage to the fuel gauge.
Be sure to check the voltage before connecting the radio. We had a problem of blowing the radio fuse when the headlights were on. It turned out to a surge in current from the alternator. I ended up finding it with my amp meter connected in-line with the wire going to the radio. I cured it by installed a slow blow fuse of the same amperage.
Really nice Original car with the Fulton visor, skirts, over-ride bumpers...almost every option except for the fog lights. Now that he's went for a few rides in my truck he decided to Street Rod it. I already built him a 350, 350 tranny, 66 Chevelle rearend, and have all the Mustang II suspension now so next month the fun begins!