Hi Freda, my little one had heat rash on her face and shoulders when she was about 4weeks, and now she is 12weeks (tomorrow!) in the humid weather the past few days she has a little on her face again.
I found it appeared in the places that got sweaty - at 4weeks she was forever being cuddled by visitors and falling asleep on the chest getting ever so hot, the rash was always worse on the side she had been sleeping. The HV told me not to bath her more than once a week and to cotton wool and warm water wash her face daily, which I did but I started to notice that by bathing her her skin started to clear up so I would bath her every evening, and after 4-5 days it was completely clear. It also helped us get into a routine and ever since then she has had her bath every evening and is in bed asleep by 7pm.
Phew! That was a bit long-winded! Either way, I know it is common for little ones to get a bit spotty and I am sure it is nothing to worry about as long as you can keep her skin clean and dry :-)
Congratulations by the way!