Edinburgh is set to see temperatures plunge to -1C on the 30 October with lows of 3C expected on the 31st.
Temperatures in Glasgow, Dundee and Aberdeen will be slightly warmer at around 4C.
Met Office meteorologist John West said: “At the moment, we have got some quite cold crisp weather with plenty of sunshine about. As we get to mid-week, it is going to be be increasingly unsettled.
“It will be likely less cold by Wednesday but by no means warm. If anybody is going to be out and about on Wednesday it might be a good idea to have a coat handy and maybe also a waterproof.”
Temperatures are set to relent next week after parts of the UK saw snow during this weekend’s autumn cold snap.
Snow was seen in higher parts of Scotland and north-east England on Saturday.
The Met Office expects showers will continue to hit North Sea coastal areas on Monday. Once any fog patches clear, it should be largely dry elsewhere with plenty of sunshine but still cold.
It should turn wet and windy across many eastern areas on Tuesday, with snow possible across Scottish hills.
Mr West said that by Thursday morning temperatures are expected to be around freezing for Scotland, between 4-5C in London and there may be a touch of frost in the north west with temperatures of around 2-3C.