After how it's been so far I think there would be a decent chance of him getting sacked despite finishing 7th, we'll need to put together some incredible form between now and the end of May for him to be kept on.
The people who do the 'hiring and firing' will look at the overall situation come summer and compare it with the situation when Koeman left. They have the knowledge of what goes on behind the scenes whereas we really only see the 90mins on the field so they will judge how far we have moved on irrespective of whether we are seeing it at games yet. If they see progress and Sam 'sells' them a plan that looks credible and in line with their vision then I suppose they may offer him a longer contract?
If they don't see sufficient progress then I suppose it's goodbye?
If I was neutral I'd be curious to see what he could do with financial resources he's never had before rather than being judged on trophies won when competing with teams who spend more on one player than he's probably ever had to spend on a whole team.
I'd feel quite happy seeing that pan out but just wish it was somewhere else where it was proved or disproved!