Ok, I'm probably wrong and confused, and I don't know what you are
measuring. In my defense, you don't seem to know what you are measuring
either.

Obviously I don't know how these line voltage themostats work. But I
suppose it is reasonable that they _are_ placed in series with the
load. And you are measuring the AMPs by just touching the two probes to
your two wires, and so are measuring the current that would pass
through your heating elements in the full ON position. I would be a
little nervous about having 10 amps or more go through the little
multimeter probe wires that I would be holding, and I know my
multimeter would blow its fuse if I tried that anyway.

The other poster is probably right, that your thermostat is going to
borrow some power using a current division circuit, and that this
requires at least a certain low resistance (and so high amps) for the
heating element. But that you are measuring 0.68 amps seems odd to me,
because an electric heater would use 5, 10, or more amps, no?. I don't
know what a hydroponic baseboard heater is (unless you are using an
electric heater to grow plants in water, that is). Is this some fancy
hot water system with electronic valves (that need .68 amps to
operate)?

It should be obvious that I am not going to be able to help you here,
but I am curious all the same.