You arrive at the temple without incident and find Brightsoul as you left him. Ajax greets him and checks his wounds and asks if he may stable him at the mansion overnight. Assuming you allow it Ajax spends the walk back telling Brightsoul of the battle, mainly telling him about Ari's bravery, Rubius archery and Asinjin's spells and also how he is glad that Brightsoul was here, safe, as linnorms, like deep dragons (wince), are notoriously fond of horse flesh.
You leave him in the stable and return to the house, leaving the sounds of Astrek and Brightsoul arguing in celestial animal speak behind you. Presumably at some point you also return the Kingmaker to Ajax.