Got some recommendations only;

-One plus One 64gb 3gb ram Ori Brighstar rm11xx

-LG G3 32gb 3gb ram AP set rm13xx

-Xperia Z2 16gb 3gb ram AP set rm12xx (no 32gb but can add sd card)

-Note 3 Lte 32gb AP set (5.7in screen)

-zenfone 2 32/64gb 4gb ram Ori Asus

Hi,

Zenfone 2 4gb ram comes with intel z3570 2.3ghz cpu..

In term of gaming, the cpu comes with PowerVR G6430 (same GPU as found in apple A7 of iphone 5s, probably only different in clock speed).. I bet that this gpu will perform as good as Adreno 330 in snapdragon 800/801 phones.. So gaming should be no problem..

Camera?
Hmm this one is a bit difficult.. Most reviews tht I read/watched mentioned tht the camera is decent not best..

Fast internet?
This phone got LTE

Memory?
U got 32gb and 64gb options..

No lag?
There will be lag of course this is android, but at minimum level.. There are so many factors to consider when we talk about lag, but I will say this phone will perform very well.. And the lag should come once in a while.. After all this phone use Asus custom UI..

Battery life?
Decent.. Not going to achieve the good endurance of z2 or one plus one la.. But should be good enough..

Temperature?
check utube video, i forgot this one..

Well u already have the answer.. U can have both cheap+flagship phone if u buy One Plus One.. No other phones could beat One plus one's price to spec ratio right now.. The closest one i think is Zenfone 2..

U want to flash custom rom with your device? samsung and LG smartphone are the easiest one..their flagship usually will have development for couple of years. sony usually got locked bootloader (can be opened with extra efforts) and HTC also like Sony if not mistaken..

Most chinese smartphones doesnt have large customer base, therefore less development.. I think only OPO, some famous Oppo and Xiaomi phones got lot developments..

Rite now, OPO is the best choice la.. But other suggestions are LG G3, Xperia Z2 (both AP set are below 1.3k)..

Zenfone 2 is ok la.. Got beast spec, but it is a new phone so of course there will be little (if any) development for it right now..

Honor 6, Mi3 (If u still able to find a new one or second hand), Meizu MX4 (gud camera)

top up for OnePlus One, Mi4, LG G3