Thermostat wire type
You'll be fine with solid wire.  Tstat wire is generally 18 gauge which is pretty small.  Also, since you'll be going thru all the work to fish the cable (which can be a PITA), I'd go with 18/7 cable.  That way, if you or the next homeowner wants to install a heat pump or A/C the cable will be in place to support that.
Edit:  Thanks for the contribution from manassehkatz-Moving 2 Codidact, I want to add to the answer:  Smart tstats also need constant power which requires an additional wire in the cable. So if the OP or some future owner wanted to incorporate that as well, the cable would be in place.  I deleted the ref to 18/5.