Im new here and new to boating. Been 15 yrs since I had my last boat. Im just spit-balling here. If you get an air pocket under the T-stat in will prevent the water from touching the T-stat and stop it from opening, causing an overheat condition. The sensor may still read low but engine running too hot. Does your T-stat have an air bleed hole in it? If not, drill a 1/8” hole in the flange. It wont allow too much water past the T-stat, but it will let air escape. It could be why it only happens at initial start When the cooling system is empty.
a strong impeller could force water past that point, but a weak impeller might have trouble generating enough water volume.