Do people with temporal lobe epilepsy have alzheimer's later?

Not necessarily: Alzheimer's is a complex degenerative brain disorder with many facets, as yet not well understood. Temporal lobe epilepsy is a definitive seizure problem whose etiology (cause) will determine future symptoms. They aren't necessarily related.

Great question: Boston is a great town to keep track of this. This is a very sophisticated question. There are rare cases of "tle" in which an autoimmune encephalitis seems to be causitive. Some cases of autoimmune encephalitis are not monophasic, and can recur, with cumulative neuronal injury. It is possible but yet unknown if alzheimer-type pathology (amyloid plaques) would be accelerated in such cases.