I need to relocate a thermostat and have the additional wire needed but I am not sure of the ideal way to "join" the cable sections.
Will using wire nuts and zip tie be good enough?
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A butt splice connector, or twist-on wire connector would be fine. Just make sure you use connectors that are designed for the size, and number of wires being connected.
Technically, you should probably either pull all new wiring, so that it's continuous from HVAC to thermostat. Or put the connections in a junction box, that is left accessible.
DO NOT use a crimp connector on solid conductors.
NASA approves crimp connectors only on stranded wire, and specifically prohibits the use of crimp connectors on solid wire (see 4.3.4 on page 23 of the link below). Solid wire should be spliced by soldering; or in the building trade, wire nuts may be acceptable.
As with anything else, consider the consequence of primary failure (the thing doesn't function as intended), and secondary failure (house freezes because thermostat failed to call for heat, or fire from high resistance due to improper connection).
BETTER CHOICE for the DIY person is a new connector from Ideal which is approved by UL, made in USA, and available at Home Depot and Amazon ... Spliceline. More expensive than soldering and heatshrink, but easier and faster for sure; although a little bulkier.