Can current flow through a relay's NO channel when it's not energized?
This is not an answer but to help you with your terminology.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. A single-pole, single-throw (SPST) relay.


The relay is drawn in its unpowered or de-energised state.
The common pole wile therefore be connected to the N.C. contact.
On energisation of the coil the contact will change position and the common pole will then be connected to the N.O. contact.



  Can current flow through a relay's NC channel when it's open (= relay unpowered)?


"Open" in the context of relays means that there is a gap between the contacts so current will not flow. However, you are trying to describe the relay unpowered in which case the N.C. contact will be closed and current will flow.


  It worked fine for weeks when testing and when actually wired up to the heating it worked for about a week but now the heating is always on, even when I explicitely close the relay. 


I think you mean "when I explicitly energise the relay".

If the heating is staying on then the contact is probably welded.


  It's even on when the pi is switched off. 


You should expect this if you used the N.C. contact.


  When I measure with a multimeter, the meter claims it's closed. 


If you measure the N.C. contact with the relay de-energised then this is the expected result.


  Could someone tell me what I'm doing wrong please?


It could be one of a number of things:


You have used an AC-rated relay on a DC supply.
You have used the relay to switch a voltage higher than the contact ratings.
You have provided no snubber across the load to protect the contacts.