Basics - help with resistance reading
35.8Ω is exactly 35.2Ω for engineering purposes, and certainly for a commercial product that just has to produce more or less the right amount of heat, something midway between 1 kW and 2 kW.
Continuity mode on a meter should produce an indication when the probes are shorted together, and not when they're not. That's the only behaviour that's guaranteed for continuity mode. Most meters will also produce an indication for small resistances of a few ohms, perhaps a few 10s of ohms, depending on how the meter designer was feeling at the time. With 35Ω, I would not be surprised at any behaviour from the meter on the continuity setting, including going on and off. Does your meter have a datasheet where it specifies what the continuity limits are? Don't bin your heater on the strength of the meter beeping.
If you want to measure what your heater element is doing, use the resistance function. That's intended to tell the difference between 35 and 36 ohms. Watch the resistance reading while you gently tap your heater, that should show up any breaks in the circuit.
Do bear in mind that equipment intended for mains use may have connectors that read open circuit when a very low voltage is applied, such as that of a DMM. Under normal use, the high voltage will break down any insulating film that has formed on the surface of the connectors from contamination in the atmosphere.