I took a look at the docs for Net::SSLeay... You're using the high-level API above; unfortunately, I don't see a way to download directly to a file with those methods. However, the module also has a low-level API, which should provide the functionality you need.

You should be able to use the Net::SSLeay::read() method to read in chunks of the file and write them directly to the output file, rather than getting the entire file at once. The documentation provides more details.