Water is conceived to undergo an acid-base dissociation:
#H_2O rightleftharpoons H^+ + OH^-#
Alternatively,
#2H_2O rightleftharpoons H_3O^+ + OH^-#
Both reactions are somewhat conceptual, in that there is no species that corresponds to #H^+# or even #H_3O^+# (aka, the hydronium ion). As far as anyone knows, this acidium ion is 4-5 water molecules with an extra #H^+#, i.e. #H_9O_4^+#; a cluster of water molecules with an extra #H^+#. Whatever it is, we conceive that the species in solution is #H_3O^+#, and we write our reactions and model our equilibria accordingly.
We can certainly write the equilibrium reaction for the above equation, because it has been extensively measured:
#K_w = [OH^-][H_3O^+]# #=# #10^(-14)#, at #298K#. Would you expect #K_w# to increase or decrease at temperatures #># #298K#?