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I'm probably being thick, but does anyone know which book has the rules for the Thunderbolt Heavy Fighter in it?

A lot of them. The most recent books should be Aeronautica Imperialis or Fall of Orpheus, though the latter is only for DKoK.

However, they also released the rules in the Death from the Skies PDF and increased the points cost of it by 25% compared to FoO.

https://www.forgeworld.co.uk/resources/fw_site/fw_pdfs/Warhammer_40000/Death-from-the-Skies.pdf

Technically it depends on which army you're playing. If you're using Krieg you need Orpheus, if you're using the IA1 Armoured Company it's in IA1, if you're using Elysians it's in IA3, if you're using the normal AM book you use the Death from the Skies update.

The rules are the same in all of them, but the cost fluctuates between them (160pts for Krieg, 180pts for Elysia, 200pts for AM).

 AnomanderRake wrote:
Technically it depends on which army you're playing. If you're using Krieg you need Orpheus, if you're using the IA1 Armoured Company it's in IA1, if you're using Elysians it's in IA3, if you're using the normal AM book you use the Death from the Skies update.

The rules are the same in all of them, but the cost fluctuates between them (160pts for Krieg, 180pts for Elysia, 200pts for AM).

I can be noted that the equipment also changes. I noticed that for Krieg, we get 6 Skystrike missiles while AM gets 4 for the same costs. And they need to pay 40 points more for the Fighter, although it also includes 10 points of extra wargear.
(They also get somewhat cheapers bombs, but I don't see anyone ever taking them).

Thanks for that.

Much more complicated answer than I was expecting!

And the Crusade Thunderbolt makes it all look a little drab by hauling S6 Armourbane missiles that reroll to hit Flyers and having BS4 besides for the 200pt base price.