I think the easiest and most straightforward way to get close to what you want is through the Weather Underground integration. This records your data in 5 minute intervals. You can pull up the data for any given date range. The default view is Graphs, but there is a Table tab that will display the data in spreadsheet format. You can then highlight the table and simply copy paste into a spreadsheet to sort and manipulate the data. Sort on the temp field ascending and descending to see the high and low.
Another option is to use the IFTTT integration. There is an IFTTT trigger for “New Observation” that will fire every time it gets a new observation (every 1 minute) and log it to a Google Sheets doc. Note, by default, IFTTT only allows 2000 rows before it creates a new sheet…which is annoying. There is a workaround if you don’t want it to roll like that. Details are here Google Sheets, IFTTT and the 2000 row limit - a query [EDIT - and Solution]