Companies have different standards depending on their by-laws and the rules and regulations that are in effect that the employees are made aware of (notification is important for compliance).
Depending on the policy regarding tardiness of your company, the employer is generally given presumption that they enforce their policies and standards in good faith through their management prerogative. If a written warning is indeed warranted, then that should be the case even if you were not tardy for the past 7 years or so.
For tardiness, there should be no termination yet, since the punishment of tardiness generally includes written warnings, verbal warnings, or suspension if shown to be habitually done. The rule of thumb is that the punishment should fit the crime. Theft of company property warrants termination, while tardiness does not hold the same weight of the offense as the aforementioned.
It is safe to say that you should not consider yourself terminated yet. If your employer will do so, then he may be faced with an illegal dismissal case, which no employer in his right mind would want to face.