Q: What happens if we use a hot-wire voltmeter in a DC circuit instead of an AC circuit? What happens when we use a hot-wire voltmeter to measure voltage across a resistor in a DC circuit?
Does it show the root-mean-square voltage or does it show the mean voltage?

A: Since a hot wire meter will inherently have a low resistance and use to measure currents of 10s of milliamps and above its use as a voltmeter is rather limited.
The scale on such a meter is non linear and would be calibrated to read rms values as for the operation of this device you are relying on the heating effect of an electric current $\propto I^2R$.  
I have just found this extract from a book which may be of use to you?
