The "Estimated" meter reading are not done in a haphazard way, it's based on two things, customer's past usage and the recent monthly "degree-day" formula of the customer service area.
What this means is, that any recent changes within a household will be unknown till two things happen...the new usage patten is realized in respect to the prior changing monthly 'degree days" and an "Actual" meter reading has been taken.
In any event the next "Actual" meter reading will be adjusted to be up to date w/ what was either over or under charged prior.
In other words...don't panic when the next few bills after a major heating system change doesn't reflect your expectations...especially in the winter heating months. But it will all work out eventually.
Our bills here will indicate whether it was "Estimated" or "Actual" .
Who's going to explain that to him.