Yeah, I also thought 懐炉. I did a silly rough translation of it now, please improve it if you feel you can. As for 父ちゃん, let's hope someone with some in-game knowledge comes along, then. :)
If there were a comma after 父ちゃん it would make perfect sense. "父ちゃん, everything's turned pink!" does match the pink background of that last panel. It'd be even better if 父ちゃん were blind or something. As it is written, though, it's a bit confusing.
isn't 父ちゃん just a way for Sazh to refer to himself as 'daddy' in the way that Lightning might call herself 'nee-san' (i.e., scene with Snow when he calls her his sister)? Adding it for now, change if you find a better way to put it.
Use...?He really is warm....However...It feels as though his body temperature is somehow rising......Well, there goes the cold, anyway.Yeah!Next, pass my sister-in-law this way again, Hope!Why don't you heat up with Hope as well?*scoop*...You're right.Please do!Light-san!Right! Hope's the replacement heater!Daddy sees pink in all directions.Thank you...Me too!...It's awfully cold today.Kids have high body temperatures, don't they?Wait!Stop it!Not you too, Vanille-san!Hey!As frail as you are, I thought they'd really break you.But he really is warm, isn't he?Maybe I should.Eh?I was only joking...If you're happy with me, then please, use me to your heart's content!......Er, right.Yes!He's awfully eager...*squeeze*...You know, this reminds me of the time in Palomporom...It's all right, at least he's warm!Don't be breaking Hope now!Thank you, don't mind me...Y—