'.. the school is clearly great for the kids except that it has no warmth, no soul.'
If this is the case, it ain't that great.
You'll wish you hadn't, I think. (Was a primary teacher for 10 years.) If the head and deputy are cold fish, this will be filtering down to their teachers. They may nail smiles to their faces, but underneath it all they're probably very pressurised and possibly isolated. It's a miserable job if you don't like your boss much, and this will be filtering directly into all the relationships in the school.
To lots of parents and OFSTED, 'great' means the kids can jump through hoops/hit the targets and have all the answers rehearsed for when the OFSTED team turn up. Ugh. How repulsive. I think all this means is that the school are teaching to the test.
Take note of what the current batch of parents say, especially those who've had issues there or intensive dealings with staff (e.g. parents of SEN children - they'll know first hand if there is any compassion in the school.) Look at what there is in the school in the displays, playground, etc to show they've got a sense of humour, pride in the childrens' achievements, and chances for all abilities to shine. Ask if you can be shown round by some of the children. Ask about what supports they offer new pupils. Ask about how they encourage children to make and keep friends (in other words, teach them not to bully). Ask about the role of arts in the school (usually very telling - OFSTED hardly rate it as important, and it's one of the most powerful teaching tools to boost childrens' self esteem, along with PE.)Try and get a peek in the staffroom and take note of how many cards/flowers/nice posters/etc there are. Does it look a bit manky to you? It will give you a tiny peek behind the scenes. I did supply for 6 months. The schools I hated the most always had the most depressing staffrooms imaginable.