Now I've read the thread properly I am back to say:
Where in Tz? If in Dar then it will be hot in Feb, but all the houses have a/c so sleeping at night and nap times is easy.
If in Arusha then it will be like Nairobi, fresh, hot in the sun, cool in the shade, early morning and early evening.
Flights are direct from Lon to Dar with a brief stop en route at Arusha. They are mostly overnight flights and at two months old is just the best time to travel on a night flight with a baby. The baby will sleep very easily.
Vaccinations: Yellow fever is only necessary from 9 months old, Hep A from a year and Typhoid from 2 years old (I have a 14 mth old!) Otherwise the baby has your natural immunity for the first 6 months of his life.
Both Dar and Arusha have pretty good medical facilities, your diplomat friends will have all the details.
Good nappies you can get easily here in Nairobi, so probably not too bad in Dar/Arusha. Formula is very expensive and the range is not the same as in the UK so if the baby is bottle fed, then I would advise you to bring your own formula.
Post CS recovery is different for everyone, like VS I am a quick recoverer and by 2 months am pretty much back to normal. Taking the babies at 2 weeks 1 to Dar and 1 to Cameroon was tiring but do-able and I was glad to be back in my spacious house with lots of help
Equipment, a car seat and sling should be all you need as I am certain your friends will be able to beg steal and borrow from one of their many friends, its always a close knit community in these places and everyone is always willing to help.
And to settle an argument, February in Kenya this year was pretty warm, around 25 degrees in the daytime, but at the moment tis blardy cold, I have the fire going!