I assume that when January 19, 2038 rolls around, there will be a plan for extending the time to more than four bytes. or is it the case that the four bytes are not UNIX time, or do not begin in 1970?
It is a Unix timestamp, but let me correct a minor detail:
The Y2.038 problem applies to a signed 32 bit number. The Bitcoin timestamp is unsigned, so it can represent the date for twice as long. Therefore, it will become a problem in 136.1 years, or in the year 2106.
Somewhen before then, there will need to be a hard fork.