Hi, I agree with John H.
Most of my FIATs have had 'poor' third gear synchro. But I treat them with respect - you know it's not too good, so you don't push it! Just an extra half-second or one second is the difference while changing gear. I notice that when someone else drives my car, they're wrestling with the gear lever, crunching away angrily... and what does it gain them? an extra second or so?
I also agree with Enzo in that a gear oil change would be a good idea, but I recommend sticking with the FIAT oil, Tutela ZC 90. It's not that expensive, and regardless of GL3/GL5 etc. it is important that it does not smell of sulphur (it is a non-EP gear oil.)
It is possible for a mechanic to disassemble the gearbox and turn over the synchro ring for 3rd/4th, this effectively gets about 1/2-extra life out of it. I would suggest this if there are any other gearbox faults, e.g. bearing noises, that make a 'quick' overhaul worthwhile. Anything more than a quick overhaul (e.g. fitting new synchros) inevitably leads to an expensive operation because there are many other parts that will also be somewhat worn, so to do a proper job everything must be replaced.
So why not just drive within its limits - you'll still get good performance really - and it should last for a long time without getting any worse.
Recently I sold an X1/9 to someone that drove it quite brutally. I had found the third-gear synchro OK, thousands of happy kilometres, but I noticed during his test-drive that he crunched it every time. Sometimes he would just shove the lever into gear with considerable force, and judging from the jolt I don't think the clutch was being used properly. Anyway, I get this phone call two weeks later. The car is immobile, the transmission stuck in third gear. The gearbox was subsequently stripped by a specialist, who pronounced that third gear synchro had 'exploded'. So that's how NOT to treat your third gear... remember, thousands of happy kilometres, or a few hundred brutally frustrating kilometres... it was the same gearbox!
PS. Double-declutching works as follows (I'm not disagreeing with yellow911turbo, just offering more detail). Normally when changing from 4th to 3rd, the synchro will speed up the 'free' shaft while clutch is disengaged, so the gears can engage. If you engage the clutch with gearbox in neutral and rev the engine, you are speeding up the 'free' shaft, then you disengage clutch and engage third. But it is easy to over-speed the 'free' shaft and then you have made work for the synchro because it has to slow the 'free' shaft down.
I put it to you also that the double-declutching takes at least a second to do properly (you must fully engage clutch with lever out of gear, blip the throttle, and fully disengage clutch again before attempting to select 3rd) and so I think it's easier to just take your time changing gears the normal way. But yellow911turbo is from Italy, and they double-declutch because they were weaned on FIAT 500s, and because they are impatient...
-Alex