Hi @Vincent_Herlemont and welcome in the MongoDB Community
!
First, I don’t see how you are going to make this works. There is such a gap between 3.2 and 4.4 that there are probably a few differences in the 3.2 dump you will get and the 4.4 dump that you need to be able to restore on a 4.4 cluster.
The doc specifies that you can only mongorestore
to the same major version of the MongoDB server that the files were created from.
So maybe it works by some miracle. But can you bet on it?
The doc also recommends to use the same version of mongodump
& mongorestore
for the 2 operations but 100.5.1 is only compatible with 4.0, 4.2, 4.4 and 5.0.
I do have a solution though but it does require to migrate to Atlas… which also has the advantage to guarantee that you will never have to do that ever again. 
The MongoDB Atlas Live Import supports a migration path from 3.2 to 4.0 and later so definitely 3.2 to 4.4 or even 5.0. This has the benefit to secure the migration.
Once you are in 4.4 or 5.0 in Atlas, nothing prevents you from taking the snapshot back home and restore on your home-made cluster. Or stay in Atlas if you prefer to stay there and avoid other troubles in the future with some other DIY or upgrade job.
Atlas provides all this kind of automation & monitoring so you don’t have to worry about it and focus on the real added value of your product.
Cheers,
Maxime.