Replace mechanical switch with electrical switch or relay I have a remote controller for a portable heater, and working on a small project to be able to control the fan on/off from an arduino with Bluetooh HM-10 module. I thought a solenoid might work by mounting on top of the remote but it doesnt have enough force, I want to remove/desolder the mechanical button and figure out a way to control it without the switch but kind dont really know what circuit 
I should use, kind of just learning how to use arduino. 

Images of remote and button traces below. 

Any idea how I could wire this up to arduino via some switch/relay circuit? Any circuit design / schematic would be helpful
I would unsolder the switch then solder in a FET in the configuration shown below. The FET will act as a switch and may be controlled with any digital output from your Arduino board. When selecting a FET makes sure you find something that will fit the foot print you have to work with on your board, and the gate-source threshold voltage is rated to handled 5V.