Depending on whether you're doing the whole route from Lisboa, if you start at the end of March, and are going the whole way, it shouldn't be a concern, except maybe for a couple of days north of Porto.
We live 4 or 5 days' walk north of Lisboa, and typically, by the end of March, we're not using much heat (in an old, not-well-insulated Portuguese house). Regular bedding suffices at night, without heat. And as you walk on, spring will be accompanying you.
Lisbon March Weather Averages
www.holiday-weather.com
Porto April Weather Averages
www.holiday-weather.com
In our area, we usually just need heat at night from mid-November to mid-February or so (mind you, we're from Canada, so maybe a bit less delicate than some...
)