Those look like Refseq transcript IDs. You can download the current version of Refseq here: Refseq vertebrate mammalian. The *.rna.gbff.gz files in this directory contain a GenBank record for each Refseq ID and should specify the latest version. You would just need to grab the 'ACCESSION' and 'VERSION' values for each record. For example:
ACCESSION XM_002714324 VERSION XM_002714324.1 GI:291395911
Another option would be to use the NCBI E-utilities. For example, use esearch to get the uid for each Refseq ID and use it again to get the Refseq ID with current latest version number.
The following returns an XML for 'NM_000014' (note that no version is specified here) containing the uid '66932946':
The following returns an XML for the uid '66932946':
This XML contains a line: gi|66932946|ref|NM_000014.4|
Telling you that currently this Refseq transcript is on version 4. Of course, you would need a script to automate this process for the number of records that you have.