Which of the following is an incorrect match?
(a)Polar bear- Eurythermal
(b) Archaebacteria- Hydrothermal vents
(c) Cyanobacteria- Thrive in Antarctic water
(d) Desert lizards- Body temperature fairly constant

Hint: These organisms can survive in a wide range of temperatures like sharks, humans, etc. i.e. they have a large-scale range of temperatures. So in this we have to check if the given term for each animal is correct or not.

Complete step-by-step answer:
The polar bear is not eurythermal organisms but stenothermal organisms. Stenothermal organisms are organisms with a narrow range of temperature tolerance like a polar bear, frog, lizards, coconut, etc. and are restricted to specific regions only. A polar bear is restricted in a narrow range of temperatures so live in a very cold icy environment. Eurythermal organisms are organisms with a wide range of temperature tolerance like most mammals and birds.
Let’s check if others are a correct match. An opening in the seafloor from which geothermally heated water flows is a hydrothermal vent. In hydrothermal vents, the seawater can reach temperatures of over 700° Fahrenheit. Methanopyrus kandleri is a heat and salt-loving species of Archaea and lives on the chimney walls of smokers in the hydrothermal vents. It gets the energy from hydrogen gas and releases methane, a process known as methanogenesis.
The upper region of microbial mats is occupied by cyanobacteria where they can have more access to sunlight. Cyanobacteria form extensive microbial mats in the Antarctic lakes, ponds, and streams.
Behavioral means Desert lizard manages to keep its body temperature fairly constant. They laze under the sun and absorb heat when their body temperature drops below the comfort zone and moves to a shady place when the temperature starts increasing. The process by which cold-blooded lizards use to maintain their body temperature is known as Thermoregulation.

So, the correct answer is ‘Polar bear- Eurythermal’.

Note: A multi-layered sheet of microorganisms (mainly bacteria and archaea) is known as a microbial mat. You can find microbial mats growing at interfaces between different types of material, mostly on submerged or moist surfaces, a few survive in deserts.