Mitigating touch current in two-pronged AC without dedicated ground
To be easily perceptible the current has to be fairly large (at least hundreds of uA). To get, say, 500uA by capacitive coupling with a 240VAC difference would require a capacitance of around 7nF, which is pretty huge. If the plate is like 25cm x 25cm and the insulation is rather thin (like 0.25mm) it's possible. UL considers 0.5mA to be the limit of perception and it's also their limit for allowable leakage in many situations. 

The other possibility that that you are using an insulation type that leaks at high temperatures and you are allowing the insulation to get very hot. This is not uncommon with sheathed heating elements. 

Your best bet might be to make the insulation a bit thicker, and find a dielectric material that transmits heat well enough that provides some separation. Even 1mm would be a big improvement. Lower dielectric constant is also better. 

I'm not addressing issues of safety or standards here, that's more-or-less a separate issue. But you definitely do not want to connect the plate to your 2-pin plug.