Hello,
I've got basically the same Iseki model, the TS1610, and there is no thermostat or housing originally installed on these. Maybe because they only operate in warmer weather in Japan? Anyway, the equivalent Bolens Iseki models sold in the US, the G192 and G194, do have a thermostat housing at the top hose on the block that includes a bypass. If you can get ahold of one of these it will bolt right on I believe. The alternative I've been looking into is an in-line type housing that can be cut into the hose. E-bay has many listings for thermostat housings (with thermostat) that start at $1.00 and go up to $100.0 depending on the vehicle. Most are flange mount that bolt to the block, but there are several that are separate in-line type. Especially for water-cooled motorcycles... but their hose connections are too small. You need about a 1-3/8" OD hose connection I believe. The bike types are closer to 3/4" O.D. Hope this helps.
Bill