I think you are on the right track if it is tripping in the middle of the night it most probably isnt a appliance i would be concentrating on fridge freezers and hot water heaters anything that is operating when the tripping occurs .
How old is the wiring in the house if its old the fault could be in the wiring, an electrician would need to check for earth faults.
I have also come across power points that have had the earth neutral on power ponts reversed by kitchen installers this works until earth leakage is installed and even then doesnt trip unless the appliance is used.
If you can live without the small hot water heater for a while turn it off as previously suggested .
