Well A little surfing will find the valve for around $75. I think the problem with the typical adjustable thermostats like you find on a residential electric
water heater, for example is that they are not rated for a moist salt
The problem with the fixed set point thermostat switches is they are +/- 8 degrees. They are however in a sealed can so not very effected by salt
air. You might try an appliance parts
counter. You would want a thermostat switch rated for 110 degrees F. Not sure they are made that low. Might be hard to find.
FYI The threshold of pain on skin is about 120 degrees F and that decreases as we age. For those above retirement
age, 100-110 degrees F. would be the most to set a thermostat at.