If you've had this sod 'installed', that would strongly suggest you paid someone to install it. That someone should be able to tell you precisely what preparation of the soil they made beforehand, including any emendments, and precisely which fertilizer they used, if any.
Preparation for sod usually involves removal of pernicious and ordinary weeds, turning the soil over, raking or spreading to level off, allowing the area to settle or consolidate, raking up the top couple of inches and applying a balanced fertilizer, then laying the sod. So before you start thinking of applying any kind of fertiizer on top, you need to establish exactly what happened prior to the sod going down. It also would not be wise to fertilize at this stage - you need to wait for the turf to root into the soil beneath before doing that.
You've said you know the gardener you employed did no preparation other than raking the soil flat, then just laying the sods on top. If you only moved in December 2015, it's hard to know what would have grown in it if it had been left, but you haven't mentioned any obvious plant/weed growth being present prior to the turf going down. As the soil itself had been untouched, then it would already have been consolidated, so hopefully, the person who raked it over didn't leave any 'soft spots', which would cause sinking in the grass in those spots over time.
Unless you want to take the lot up and start again, then just carry on watering copiously and frequently, particularly with such high temperatures. Once it's taken root and starts growing properly, that's the time to add a lawn fertilizer. Sometimes the grass grows even before the sods have rooted into place, so just check by trying to lift a bit to test, preferably in the middle of the sodded area rather than the edges, don't pull it too hard, just see if it lifts up easily. If it doesn't, its rooted in. Rooting into the soil beneath, at this time of year, should take place pretty quickly.
To be fair to the gardener you employed, if the sods were already on the property, waiting to be laid, he didn't have much choice but to lay them immediately, with minimal preparation, though he could have applied some fertilizer. It's usual to do the soil preparation first, then wait a week, check the area, then order the sods, spreading general purpose fertilizer underneath just before laying.