My suggestion is to get it back asap.
From experience Heuer Service is way overpriced, they don't do an adequate job and they will replace parts. The last thing you want is parts replaced on a mint and rarely worn watch.
Send it to an independent watchmakers that understands vintage and make sure he does not replace any unnecessary parts (hands, crown, pushers, dial).

I had a recent watch serviced at Heuer (by the seller not me) and they replaced the crown, pushers and hands even though it was absolutely not necessary. To add insult to injury, the new parts, although genuine Heuer parts do not match the original parts. And if that wasn't bad enough, now the hours sub-dial will not reset properly.

: Hi.
: I need some advice.
: The short story is, just got a autavia 2446c from a family member.
: He bought it in 68 used it for a couple of years then been in a
: locker the past 40 years.
: To me it looks mint but i wanted to check out the condition on the
: movement so i took it in to the local watchmaker.
: He sent it down to Heuer in switzerland and now i got a suggested
: service price on 2000€. The movement runs smooth and keeps
: time as good as my omega smp. So my question is, is it worth
: spending the money on the watch?
: serial 109XXX
: Thanks
: Tony