Yes, 350g is too small to survive hibernation. http://www.britishhedgehogs.org.uk/pdf/Hibernation-Weight.pdf
I have just written the following for someone else so will copy here as much of it may be relevant to you, too.
‘You should be able to get the number of someone local, who will be able to help if the little one needs over-wintering, advise about weights in relation to local conditions, etc. from the BHPS (01584 890801). If you do catch the hoglet, try to get advice before releasing it, because sometimes it is more difficult to catch them a second time.
If you need to keep a hog in over night, use a high sided box or pet carrier as hogs are very good at escaping. You can use newspaper as a base and torn up paper (or hay, if you happen to have some around) for bedding (enough for them to hide in) and supply food and water (although they may very likely spill that!). It is useful to have scales and potential night accommodation ready before you try to catch a hog, just in case, to cause them minimum stress. So you can literally just catch, weigh and put in the box (if necessary), or release.
If there is one hoglet around, it is quite likely there is more than one, so keep an eye out. Small hoglets were arriving here, last year, until the end of November, so it’s a good idea to keep supplying food and water after you think all the hogs have disappeared.’