IPCC projections are for an ice free Arctic in September roughly near 2050. However this is under rcp 8.5, which I consider quite unlikely. Rcp 8.5 requires that the current rapid growth of renewables never gets high enough to make a difference. It also requires that climate change never has an economic impact significant enough to noticeably slow 'Business as Usual'.
This paper contains projections of arctic for RCP 4.5 - with 9 out of 14 models becoming ice free by 2069, and 3 of the models never becoming ice free. There is also a statement that the Arctic becomes ice free in September at 2.4 deg of warming (with a range from as low as 0.4 up to 6.2), and in March at 8.2. If I split the difference I get 5.3 degree of warming for ice free in June. Even RCP 8.5 does not get to about 5 degree of warming around 2150. Although the upper end of RCP 8.5 does get there around 2100.
Another way to estimate June ice free is by noting that we are currently about 30 years behind September for historical trends. For RCP 8.5 I would expect this difference to be roughly maintained, so June ice free could be reached for 8.5 around 2080. But under 4.5 or 6 I'd expect the slow down in forcing to increase the 30 year gap significantly.
As a side point 560ppm is achieved in rcp 8.5 about 2050, but is never reached under rcp4.5, and just barely reached in rcp 6.0. Unless we follow 8.5 there is an extremely wide possible range for when we get there.
Finally there is the point of ice free once vs ice free consistently. I believe the model projections are a reasonable prediction of when we might see consistent ice free conditions. I suspect rcp 4.5 is a little optimistic and that rcp 6 is more reasonable, but could only find the rcp 4.5 projection. I'll guess rcp 6 may see ice free somewhere between 2050 and 2075. However year to year variability could see at least one nearly ice free year (<1,000,000 sq km extent) between 2020 and 2040. I do have a suspicion that perfect melt conditions could see nearly ice free any year from now (and perhaps back as far as 2008), but variability observed to date doesn't seem large enough. There is the possibility that variability grows as ice gets lower....