Weatherzone meteorologist Robert Sharpe said a high pressure system over central Australia is moving across New South Wales and was going to hold off the bitterly cold temperatures in the Riverina for the first few weeks of June.

He said this high pressure system was expected to give way after this fortnight, and high winds, dry air and clear skies should eventually see temperatures creeping closer to zero in Griffith later in the month.

"The second half of June we're more likely to see cold fronts and we're also more likely to see frost," Mr Sharpe said.

"The strong high pressure system is going to be blocking the majority of cold fronts over the first two weeks."

In the meantime, Mr Sharpe said Griffith has been experiencing heavy fog in the mornings and evenings as a result of the moisture in the air from the rainfall on the weekend.

He believed the fog in Griffith shouldn't get any thicker than the past few days, but still expected to see heavy fog in some of the surrounding areas.

Griffith Council road safety officer, Greg Balind, has warned motorists to be extra careful while driving when the weather makes visibility difficult.

"Drivers need to turn their lights on during the inclement weather and need to slow down," he said.

"The speed limit may be 50 or 100 but when conditions change, you need to change your behaviour.

"Most crashes can be avoided by exercising extra caution. Slowing down that extra 10 to 20 k's might take longer but it gives you a greater chance of reaching your destination."

Griffith should experience a minimum of four degrees by Friday and across the weekend.

Mr Sharpe said that heavy frost only really tends to set in once the temperature drops below two degrees.