In reply to Gone for good:
Pau to Bagneres du Luchon was the route of the 2012 Etape du Tour, taking in the cols of Aubisque, Soulor, Tourmalet, Aspin and Peyresourde - that was 200km. It's a pretty big day out, given the hills, and you will be shagged arriving in Pau.
Apologies for stating the obvious, but even if it's roasting in the valleys, it can turn pretty cold at the summits and the wind chill coming down at speed on a sweaty body is potentially dangerous - one of our party was the last to finish that year and was nearly hospitalised with hypothermia.
Pau has a good station, but I'm afraid I don't have a clue about the trains from it.
The Tourmalet also featured in the Pau-Hautacam 2016 edition - had 2 days of blistering sunshine followed by emailed weather warnings and a miserable ride over it in drizzle!
Incidentally, an ex colleague was a native of Pau and couldn't believe anyone would want to cycle over the Tourmalet once, let alone twice