Probably temporary tinnitus, how to get rid of it?

I think you should have the ear cleaned yes. Wax removal doesn't usually remove tinnitus completely, but it can reduce the perceived loudness of it. In your case, with a very faint tinnitus, I wouldn't be surprised if it became a total non-issue after wax removal in most situations.

Do you feel like your left ear is currently blocked by the wax?

While chronic tinnitus resulting from wax removal is very rare ( http://www.tinnitusjournal.com/detalhe_artigo.asp?id=462 ), I did get permanent tinnitus from ear syringing.

From the above article:
"Only 11 patients (0.46%) of 2,400 who visited this tinnitus clinic between 1986 and 2000 reported that their tinnitus began as a result of cerumen removal procedures performed by clinicians."

There's also some suggestions regarding the safe removal of wax in the article. It's a good read.

 

I don't think wax can actually cause tinnitus.

I'd say the case often can be that there's an underlying very faint tinnitus that isn't usually heard, but if ear wax causes blockage in the ear, then that can cause the underlying tinnitus to become apparent and audible. Once the excess wax is removed, hearing returns to normal and tinnitus stops affecting that subgroup.

So in that sense it's temporary tinnitus that is only audible when there's excess wax.

There's several methods for removing ear wax. Some were mentioned in the aforementioned article I linked to.

You could first try some ear drops that are meant for this. Sometimes it's enough to remove the wax. If you have dry wax, these type of drops can soften the wax and then it's easier to remove when you go to the doctor's appointment.

In Finland this product is popular: http://www.itsehoitoapteekki.fi/Tuotteet1/muut-tuotteet/Remo-Wax/
It contains: Allantoin. 3 mg, Benzethon. chlorid. 1 mg, Butylhydroxytoluen. 1 mg, Phenethanol. 5 mg, Acid. sorb. 2 mg, Glucos. liquid., Lanolin. ol., Mink oil., Constit. et emulg., Aq. steril. ad 1 ml.


Movement of the jaw helps the ears' natural cleaning process. The American Academy of Otolaryngology discourages earwax removal unless excess earwax is causing health problems.[19] While a number of methods of earwax removal are effective, their benefits as compared to each other is not yet determined.[20] A number of softeners are effective; however, if this is not sufficient,[20] the most common method of cerumen removal is syringing with warm water.[21] A curette method is more likely to be used by otolaryngologists when the ear canal is partially occluded and the material is not adhering to the skin of the ear canal. Cotton swabs, on the other hand, push most of the earwax farther into the ear canal and remove only a small portion of the top layer of wax that happens to adhere to the fibres of the swab.[22]

http://en.wikipedia.org/wiki/Earwax#Treatment