This is a really good question, not least because it has an obvious parallel in real life: what will WE be like when we get to Heaven?

I think the first thing that will happen to Puddleglum will be that he will meet Aslan. As far as we know, he never met Aslan during his mortal life, yet he still had a strong faith in him (arguably stronger than Eustace or Jill who had met him). So perhaps we can draw some conclusions from looking at how other people reacted when they met Aslan:

1. The Pevensies and Trumpkin in "Prince Caspian", when they were trying to get to Aslan's How. Lucy knew all along that Aslan would arrive to be with them and saw him very quickly. Edmund's faith in Aslan wasn't quite as strong, but he had faith in his sister which carried him through. Peter was a bit slower to get there as he was trying to be the leader. Susan took quite a while, but when she finally did meet him he told her, "You have been listening to fears. Come, let me breathe on you" and her courage returned. Trumpkin, the cynic from the start, was presented with incontrovertible evidence that Aslan was real and became a firm believer.

2. Emeth in "The Last Battle". He had been looking for Tash all his life; but the "Tash" he'd been told about was a kind, merciful, loving saviour, which was everything that Aslan was and Tash wasn't. Aslan told him, "All find what they truly seek," and Emeth found in Aslan what he'd hoped to find in Tash.

3. Digory in "The Magician's Nephew", when he looked directly into Aslan's eyes and pleaded for something to cure his mother, only to discover that Aslan felt for her even more than he did. I think Digory learned that some of his reasons for wanting her to be cured were selfish: witnessing her dying made him feel bad and he didn't want her to leave him alone. Aslan taught him that grief is great (not great as in wonderful, great as in huge) and there were worse things than losing a loved one in death. When Digory understood this, his wish was granted.

So I think the common theme is that when people meet Aslan (in a positive way - not like the White Witch!), they find what they were really looking for, deep down, even if that wasn't what they thought they wanted consciously. In the case of Puddleglum, I think that would be reassurance that things are going to get better and better and better and that his fear no longer applies. (Bear in mind that other Marshwiggles considered Puddleglum to be too optimistic!) Yet I think his intelligence and sense of humour won't be affected, just redirected.

Gosh, I think I've learned something trying to compose this answer!