It actually helps, it gains more size and strength, if it hits the akainu's main body it can burn the akainu itself.
And that's the whole point of the discussion, akainu's magma doesn't make it immune to flames, it can be injured by them when hit directly, with kaido's size + haki + temperature makes kaido a hot iron ball with HAKI.
The temperature will burn akainu's body because it's something hot. This doesn't make much difference to a hot sword covered in haki.
On the energy issue, Ace literally solidifies his flames with HAKI as opposed to burning BB, they pierce him:
The fact that Blackbeard manages to catch the flames in the sequel means something solid.