Generally we won't address post harvest storage related problems in this forum (we only deal with specific problem related to growing food crops).
Normally the fresh thyme can be stored in refrigerator for a few days (one or two weeks) if it is warped in a damp paper towel and place it in a plastic bag. For long term storage the fresh thyme should be washed, trimmed/ chopped and dried properly before placing it in heavy freezer bags and freeze it. Make sure the material is constantly frozen at 0°F to keep it safe for a long time.