I want to replace fireplace millivolt switch with relay

[cseevinck]

This is my first time posting of this board. I am not sure I have the correct place, please advise if I should repost on a different forum.
I have a gas fireplace with a thermocouple that is controlled by a millivolt switch. I have had to replace the wall mounted switch a number of times because the resistance increases over time (contacts getting dirty or whatever). I would like to use a regular switch on the wall that is not as sensitive as a millivolt switch and have the switch throw a solid state relay that will close the circuit for the thermocouple. The regular switch end would be powered by a battery or a transformer. If I get this working I will try to connect a smartswitch to drive the powered end so I can turn the thing on using my phone or a remote control. But my first interest is to get rid of the milllivolt switch.
Any pointers will be appreciated.   

[jmelson]

A solid state relay will not operate a millivolt system.  The thermocouple/thermopile only generates about 600 mV DC, typical SSRs only work on AC and drop more than 1 V.  It is remotely possible this could actually be done with a power MOSFET.

Jon