At first I thought you meant $2k. Reading that line again I see you want a small, light laptop. 2kg is around 4 or 5lbs which is really light for a laptop. I wouldn't be surprised at all that such a small laptop would have cooling issues with the new i5 and i7s. I think I personally would shoot for a heavier laptop, or get one with the 1060/1070, but a lower i5.
My GF's daughter got a surface 3 I think. Should have been a good unit, but she got one with the i7 in it and it's had nothing but problems. You can't put the highest end things in tiny spaces and expect it to work great every time. As I've heard, i3 and i5 surface units work great. Not so much for the i7 units. But I wasn't consulted at the time because I was mom's BF. What do I know right?