Yes, a ballast resistor will certainly get hot when the ignition is on and the engine isn't running. It should be a little less hot when the engine is running.
Worst case, the resistor is passing 4 amps (12v / (1.5 ohm ballast + 1.5 ohm coil) = 4 amps). One power formula is simply Watts = V x amps. So, there will be six volts across the resistor and 4 amps = 24 Watts (6x4=24). Turn on a 15 or 20 Watt light bulb and try to grab it, that will put things in perspective.
With the engine running there isn't current flowing all the time (reduced duty cycle) so the resistor will have time to cool a bit. It will certainly still be warm.