We investigate how a temperature reduction in z−direction influences the switching probability and the noise in heat-assisted magnetic recording (HAMR) for a bit in bit-patterned media with dimensions d = 5 nm and h = 10 nm. Pure hard magnetic bits are considered and simulations with a continuous laser pulse are performed using the atomistic simulation tool VAMPIRE. The results display that the switching behavior shows a thermally induced exchange spring effect. Simultaneously, both the AC and the DC noise increase. Additionally, we illustrate how an artificial Curie temperature gradient within the material can compensate the HAMR performance loss due to the temperature gradient. Further, due to the graded Curie temperature, DC noise can be reduced compared to a structure where no temperature gradient is considered.