At higher temperatures, enzymes can become denatured, meaning that their three-dimensional shape is altered and they lose their ability to function. The rate of denaturation increases with temperature, so as the body temperature increases, the activity of the enzymes also decreases.

The specific temperature at which this occurs can vary depending on the specific enzyme, but in general, a 1-2°C increase in core body temperature can cause denaturation of some enzymes. A core body temperature of around 41°C can be life-threatening, and at this temperature, many enzymes can become denatured and stop functioning properly.

In the case of hyperthermia, the elevated body temperature can cause denaturation of enzymes involved in cellular metabolism, leading to a decrease in metabolic rate. This can result in decreased energy production and decreased efficiency in cellular processes, leading to potential cellular damage and dysfunction.

Additionally, hyperthermia can affect the activity of enzymes involved in the regulation of body temperature itself. For example, hyperthermia can impair the activity of heat shock proteins, which help protect cells from heat stress, further exacerbating the effects of elevated body temperature.

At low temperatures, the movement of the enzyme molecules becomes sluggish, and their ability to bind to substrates and catalyze reactions decreases. This results in a decrease in the rate of chemical reactions, which can have a significant impact on the functioning of the body. For example, enzymes involved in energy production and metabolism become less efficient, leading to decreased energy production and an increase in fatigue.

Hypothermia occurs when the core body temperature drops below the normal range of 36-37°C. As the body temperature decreases, the activity of enzymes decreases as well. This can result in a slowing or cessation of many physiological processes, including cellular respiration, metabolism, and cellular function.

An increase in temperature can cause the phospholipids to become more fluid, which can increase the fluidity of the cell membrane - more than normal. This can increase the permeability of the membrane, allowing ions and other small molecules to move more freely across the membrane - more than what's required to maintain a constant internal environment. 

This increased permeability can lead to the loss of ions and small molecules, leading to cellular dehydration and altering the normal ion gradients across the membrane. This can disrupt normal cellular processes and contribute to the development of cellular damage.

(So, the cell could be spending energy on active transport of ions, but membrane that's too permeable could undo the work done by active transport). 

This increased fluidity can also affect the function of membrane proteins, which are embedded in the lipid bilayer. In extreme cases, high temperatures can cause the lipid bilayer to become so fluid that it can break apart, leading to a loss of membrane integrity and cell death.

When the body temperature decreases, the phospholipids and therefore the cell membrane becomes less fluid. This can lead to changes in the permeability of the membrane, making it more difficult for ions and other small molecules to cross the membrane causing disruptions in normal cell function.

For example, changes in ion gradients across the membrane can interfere with the normal function of ion channels and transporters, which play critical roles in maintaining cell membrane potential, transmitting nerve impulses, and transporting ions and other small molecules into and out of the cell.

This decreased permeability can also affect the function of membrane proteins and enzymes, which may become more rigid and less able to perform their normal functions. In extreme cases, low temperatures can cause the lipid bilayer to become so rigid that it can no longer maintain its integrity, leading to cell damage or death.

For example, hypothermia can also disrupt normal membrane-associated enzyme activity, which can interfere with a wide range of metabolic processes. For example, enzymes involved in the breakdown of glucose to produce ATP may become less efficient, reducing the cell's ability to produce energy.