77 is fine. Plenty of houses around here have have no AC and it's warmer than that and everyone's babies are fine.

I honestly think our thermostat isn't accurate, and yours may not be either. We keep ours at 76, which is t-shirt and jeans comfortable - maybe even a hoodie if you're not moving around too much. The advice our pediatrician gave us is whatever feels comfortable to us, dress the baby the same way plus an extra light layer over top.

As for the iron levels - I'm a guy, eat plenty of meat, and take vitamins, so I doubt my iron levels are low, I just think thermostats aren't as reliable as they claim. When the AC temp is 74 or below, I need to wear a sweater constantly in our apartment. If it's 74 outside, low humidity, and I'm in the shade...I'm comfortable in shorts, so I don't trust that the thermo is accurate.

Anyway, the easiest way to check if your baby is hot to is to check behind their neck. If it's sweaty and hot, your baby is probably too hot. If it feels fine, don't worry.