ATS (Advanced Thermal Solutions) has a series of the Heat Sinks ATS-5xxx-C1, which come preassembled with high performance TIM (Thermal Interface Material).
This TIM is an adhesive, and adhesive has a shelf life
The TIM used in this Heat Sinks ATS-5xxx-C1 series is T412 which is Parker-Chomerics product.
This information can be found on manufacturer website for each and every p/n which has an adhesive
For example, for the p/n ATS-54170K-C1-R0 (ATS1213-ND), the link is:
https://www.qats.com/Search/HeatSink/503.aspx#
The shelf life of T412 is 12 months as per the Data sheet of T412
However, as per the manufacturer:
“Thermal adhesives, such as Chomerics T412, have a shelf life of 1 year when on a roll and not applied to the heatsink. Once applied to the heatsink, there is no expiration date”