You may end up with a very effective device to convert metallic copper into copper oxide if you are not careful. Bare metal, of any sort, will happily convert back to its oxide form when water is present, and especially when water and electricity are present. Exceptions of course are Gold and Platinum.
A simple resistor could do the heating. A 5W or 10W resistor. Say you have a 5V supply and you want 5W of heat, then W=IV so you need a 5V 1Amp supply. V=IR so V=5, I=1 so R must be 5 ohms. Closest is 4.7 ohms. Turn it on and off with a mosfet or transistor using one of the standard picaxe control circuits in the manual.
This should work great for a few months. Then the copper will start corroding, the resistance will go up, and the readings will become less useful.
Even though gold and platinum don't corrode, there is another cheap and cheerful way of detecting conductivity, and that is to use a huge amount of iron and accept that corrosion will happen but plan that it will be slow enough not to worry about. Eg a couple of big steel wood screws eg 1/2" in a piece of wood 10cm apart.