>>
Using a 7805 in a vehicle (basic circuit with 1 inline rectifier diode,
then small cap on input of 7805, 33uF on output).
The max calculated current draw for the circuit is approx 200mA.
Hardly seems like enough current to strain the regulator (1Amp),
but it gets hot enough that I cannot leave my finger on it for more
than 5-10 seconds.

Should it get this hot?
<<

Do the math.  You left out a lot of particulars, so I'll assume 14V going
into the regulator.  That leaves a voltage drop of 14V - 5V = 9V.  9V x
200mA = 1.8 watts.  Yup, that'll toast your finger assuming a TO-3 package
without a heatsink.


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