Viscosity is a measure of how easily a given material will flow. One way to look at it is how "syrupy" is the material. A liquid such as water has a low viscosity while molasses has a high viscosity. Viscosity is related to the temperature of the liquid. For example, syrup just taken out of as refrigerator will have a much high viscosity than the same syrup after it has been heated in a microwave before using on your favorite pancakes. Therefore, when measuring viscosity, the temperature at which the viscosity was measured needs to be stated.
Viscosity is also used to describe motor oils used in cars and trucks. Motor oils with a low viscosity will still flow even when the ambient temperature is low whereas motor oils with a high viscosity will get very thick when the temperature gets very low.
This change in viscosity is why in very cold climates, like Alaska in the winter time, trucks keep their engines running all the time. If they left them off overnight the oil would be so thick and viscous that the engine would not start.
At the other end of the temperature spectrum, as you increase the temperature for a given oil you will reach a point where the liquid starts breaking down and no longer works as intended. You could consider this the maximum temperature of viscosity for that material but it would be different for every liquid.
The only way to determine the maximum temperature for a particular substance would be to test it in a lab and see when it starts breaking down.
There appears to be some confusion in the question asked.
Viscosity and temperature are measures of two quite different physical variables. There is nothing like temperature of viscosity, and therefore nothing like maximum or minimum temperature of viscosity.
Viscosity is a measure of the resistance a liquid or gas offers to its flow. The substances that flow easily have low viscosity while the ones that are kind of thick and flow comparatively slowly have high viscosity. Viscosity of a substance depends on chemical composition of the substance as well as some other physical factors including temperature. In liquids the viscosity tends to reduce with increase in temperature. In gases the viscosity reduces with increase in temperature.