Hi Karen… A while ago I watched a temperature test on fb for Queen of hearts buttercream – they iced a cake then left it in the sun for a while and it still looked fine (you can go to their page for details). While I can’t give out their recipe as it’s in their book/ online at pretty witty cakes I can tell you a few things in general I’ve learnt about bc and heat from other sources -
Use 1/3 or so trex in place of that part of the butter to make it firmer
Minimise the liquid in your recipe as much as possible if it’s going to be hot
Use only a thin coat of bc on the edges to minimise the chances of it melting and slopping about
Generally crusting bcs have a ridiculously high proportion of sugar to butter, 3 to 6x in volume, that’s what makes it crust. The winbecklers from Cakesuppliesplus.com have a YouTube video showing how they make their bc but it’s all shortening which imo doesn’t taste as nice, and they use a fair bit of water – lots of recipes for American buttercream out there you could try – I’ve tried one by Serious Cakes which is quite nice, you can Google it.
Other than that you can also chill the cake before delivery, take it in a car with AC which should help, and of course don’t put it in the sun lol… If possible try to get a fan or portable ac unit near it. Hope that helps xxx