The switching probability of magnetic elements for heat assisted recording is investigated. It is found that FePt elements with a diameter of 5 nm and a height of 10nm show, at a field of 0.5 T, thermally written in errors of 12%, which is significant too large for bit patterned magnetic recording. Thermally written in errors can be decreased if larger head fields are applied. However, larger fields lead to an increase the fundamental thermal jitter. This leads to a dilemma between thermally written in errors and fundamental thermal jitter. This dilemma can be partly relaxed by increasing the thickness of the FePt film up to 30nm. For realistic head fields, it is found that the fundamental thermal jitter is in the same order of magnitude of the fundamental thermal jitter in conventional recording, which is about 0.5 -0.8 nm. Composite structures consisting of high Curie top layer and FePt as hard magnetic storage layer can reduce the thermally written in errors to be smaller than 10 -4 if the damping constant is increased in the soft layer. Large damping may be realized by doping with rare earth elements. Similar to single FePt grains also in composite structure an increase of switching probability is sacrifices by an increase of thermal jitter. Structures utilizing first order phase transitions breaking the thermal jitter and writeability dilemma are discussed.