It's 55-57 minutes on the Piccadilly line (Tube) from Heathrow to King's Cross St Pancras, and yes it should take that (unless there's some snafu).

Sounds like you've got a plan of sorts, just to say that St Pancras is on the edge of central London and just oing for a walk about on the Euston Road (the main road that the station fronts onto) would leave you with a somewhat skewed idea of what London's really about!

I dunno how far you're prepared to walk, or whether you'd be up for jumping on a bus, or on one of the new(-ish) hire bicycles (aka Boris Bikes), whether you'd be leaving your luggage at the left-luggage place at St Pancras or keeping it with you or what. However off the top of my head I might suggest a wander (or indeed a cycle) around Clerkenwell, Holborn or Bloomsbury (or some combo thereof) - Camden Town is also not far north west of St Pancras, but it'd be pretty dead at that time in the morning.

Indeed if you are up for a bit of a stretch of the legs then a better idea might be to get off the Tube early at Holborn or Russell Square and then walk up from there (up Judd Street - and if coming from Holborn I'd deviate slightly and go along Montague St next to the British Museum to Russell Square then up Judd St). Or get off the Tube even earlier at Covent Garden, have a wander around and perhaps breakfast (at Joe Allen's maybe?), then get the 59 bus up Kingsway to St Pancras. All depends on the luggage issue I suppose.

The walkit.com website is useful for walking route and getting an idea about the distance and time. And here's a streetmap centred on St Pancras.