It might be worth just taking her over the vets for a quick check up. Although its not uncommon for young kittens to cry when they first go to their forever home away from their mum and siblings, what is unusual is for the kitten to settle in for a few weeks and then start crying.

Are you sure the kitten is not hugry at night? Kittens eat alot, they need alot of energy to grow, at 15 weeks, I would be inclined to allow the kitten to eat as much as it likes, so make sure there is food available.
Also, if the kitten is eating dry food, it will need lots of water, make sure the kitten has acess to this too.

I would try not to make a habbit out of letting the kitten sleep in your bed unless you plan on letting it sleep in your bed forever. You know what they say, old habbits die hard.

Cats are generally most active during dawn and dust, as this is when they would be out catching prey, use this to your advantage, and 'play the kitten hard' during the evening to try and tire it out. But be aware, with the light mornings in the summer, the kitten is likely to become active fairly early in the morning too.

Try getting some toys that 'play back'. For example, in sainsburys they do toys on elastic that you can hook over a door handle, because its on elastic, everytime the kitten tugs it, the toy will tug back, this might keep the kitten enteraind without you haveing to drag toys around the room. There is also a mouse on a spring toy in wilkinsons, but that one squeeks, so not so good if you are trying to sleep.

I know you have tried the hot water bottle, but what about getting a radiator bed? The other thing is for some reason my cats all love to sleep on towles, if you have an old bath towle or something try using that in its bed, might find that more comfortable.

Does the kitten have any other unusual behavior?
It may be worth you contacting the breeder to find out if any of its litter mates are having problems.