Are the drain current I_D and I_DP (absolute maximum ratings) constant to temperature?

The thermal resistance of the package and the maximum channel temperature listed in the datasheet are largely related to the allowable range for each product. In addition, there may be limitations due to the current capability of the package and the safe operation area.

The drain current I_D・I_DP listed in the datasheet are specified under ideal heat dissipation conditions of 25°C ambient. I_D indicates the maximum rating of the forward-drain current when DC is applied. I_DP is rated for the forward drainage current at the specified pulse width.
These currents are set so that the channel-temperature does not exceed T_ch (max) when MOSFET is operating in the on-region (linear region) under specified conditions.
P_Rloss of power dissipation due to the drain-to-source on-resistance, R_DS(ON) is the major factor causing MOSFET to rise in the on-region.
As an example, find the forward drain current I_D when DC current is applied.
The loss P_Rloss due to the on-resistance R_DS(ON) is given by the following equation.

P_Rloss = R_DS(ON) x I_D²

Assuming that the thermal resistance of the product is R_th(ch-c), the temperature rise ΔT due to the heat generated by the loss is given by the following equation.

ΔT = P_Rloss ｘ R_th(ch-c)

The channel temperature is obtained by adding ΔT to the case temperature T_C during MOSFET operation, so the following equation must be satisfied.

T_c + ΔT < T_ch(max)

Solving the above formula for the I_D gives: I_DP can be considered in the same way.

The following documents have relevant information: Use this as a reference.