A metal halide lamp (101) is described, the lamp being designed such that, when the lamp is operative in a vertical orientation, the location of the salt pool is close to the top of the discharge chamber (5). In an embodiment, the coldest spot is close to the top of the discharge chamber. Means are provided enabling more heat to be supplied to the bottom part than to the upper part. In a lamp assembly (10), comprising a lamp (101) arranged inside a bulb (11), additional heat generating means (90) may comprise a radiation coil (91).