Glen, not sure about the Kendrick dew heater controller but most of the dew heater controllers switch the negative/ground terminal. This normally would not be a problem but most of heating tapes use the
RCA plugs which have one terminal (usually ground) exposed.
The combination of the two (switching ground and RCA plugs) is very bad and potentially dangerous. When the heater ground gets switched off the outside of the RCA plug will be at 12V. Due to the design of the RCA plugs (large exposed metal surface) it is just too easy for the 12V to touch the scope or the mount somewhere. This will put everything at 12V potential.
Unfortunately almost everybody is using the same bad design. Try wrapping something around the dew heater connectors to insulate them.