Will said:
"You have to keep in mind the current surge there until the heater warms up.
The colder the heater is, the more current it draws. I would use a conductor
with at least 750 cir mils per ampere. For 3 amperes, that equals out to be
about 16 AWG wire for the minimum"
The filament choke should not take into account any surge current, and there
is an advantage in limiting the wire size to limit surge current. By
limiting the wire size, the smaller wire will limit the surge current and
protect the tube. Since the choke is presumably in the slipstream of air, a
significantly smaller size of wire can be used. If there is no other means
to protect the filament surge current, then this is an opportunity to
protect the tube and wind a smaller choke.
Since chokes always seem to be just large enough to not fit where you want
them to, take advantage of downsizing.