Working Principle of a Transformer

But if there is a resistance in the primary coil it will dissipate heat following $I^{2}×R$ (primary).

For an ideal transformer energy is conserved. Power in primary = power in secondary. Therefore there can be no resistance in the primary coil or there will be energy dissipated (lost) as heat in the primary coil. So for an ideal transformer the primary and secondary coils are ideal inductors.

The equation you have written is intended to give the impedance seen at the input to the transformer primary, $Z_p$, not the resistance of the primary coil. The impedance seen at the input of the primary coil is then a function of the impedance (load) of the load, $Z_L$, connected to the secondary, or

$$Z_{p}=biggl(frac{N_p}{N_S}biggr )^{2}Z_L$$

Note that for an ideal transformer, where the primary and secondary coils are considered ideal inductors, the impedance of the primary coil and secondary coils themselves is considered to be purely inductive reactance, i.e., having no resistance.

Hope this helps.