Caecilius submitted this idea :
Even the 600W ones can generate more heat than they can dissipate and
so do 'overheat' and then cycle on their overtemp stats, way before
they may have reached the temp set by the main thermostat. I even
considered (and may well try this year) or rigging up two sockets on
an extension lead and wiring two of the 600W heaters in series so they
become two x 300W heaters. Set one stat on Max and then use the other
to manage the actual room temp.

That's useful information. I was considering replacing the convector
heater with a oil-filled rad to smooth the output by increasing
thermal mass, but I don't think I'll bother now if that's how they
work.

If an oil heater is used in too large a space, set on too high a
temperature, then they will cycle on their over heat stat. You are
basically asking them to do more than they are capable of doing.