Where is the thermostat on a 1997 Johnson outboard motor?

It depends on the particular engine in question. Most models locate the thermostat(s) in the cylinder head(s). They may, depending on the model, be situated in the top, or the bottom portion of the head. The exception would be a V4 model, in which the thermostats are enclosed in a housing located on the backside of the adapter plate, between the heads. The housing is easily identified by the water passage hoses running to the cylinder heads.