From the latest (1999) data I could find from the AMA, approximately 23% of surveyed surgeons were 'employees' of one sort or another which would include academic centers and hospitals. About 42% worked in private group practice. The remaining 35% worked in solo private practive.
Of those that were employees (23% of the surveyed surgeons) the distribution were as follows:
6.1% HMO, 34% free-standing medical center, 7.4% private hospitals, 35% medical schools/universities, and 13% for government hospitals.
This is for all surgeons. They did not have cardiothoracic surgeon as a specific subset (although they did have some surgical specialties separate such as ENT, Ophtho, etc.)