Computing monthly mean daily minimum and maximum temperature

ERA5 daily data can be retrieved with their Daily Statistics Calculator, but it is difficult to download a lot of data with it (documentation here). Based on the information you gave me, I provided an example below that works in Python (Jupyter). Unfortunately, you aren't allowed to iterate over multiple statistics, so you'll have to merge the min and max data together at some point after download.

The following code will download .nc files of daily minimum and maximum 2m temperature monthly for 2020 - 2021 (where daily values are calculated assuming UTC+00:00 over a 1 x 1 degree grid for the whole globe):

# Import and launch CDS API
import cdsapi
c = cdsapi.Client()

# Specify the directory where your files will be saved to 
path = '/path/to/files/'

# Set parameters
dataset = 'reanalysis-era5-single-levels'
variable = '2m_temperature'
months = ['01','02','03','04','05','06','07','08','09','10','11','12']
years = ['2020','2021']
statistics = ['daily_minimum','daily_maximum']

# Loop parameters by statistic, month, then year
for year in years:
    for month in months:
        for statistic in statistics:
            print('Running: '+statistic+' '+variable+' '+month+'-'+year)
            params={
                'realm':'c3s',
                'project':'app-c3s-daily-era5-statistics',
                'version':'master',
                'kwargs':{
                    'dataset':dataset,
                    'product_type':'reanalysis',
                    'variable':variable,
                    'statistic':statistic,
                    'year':year,
                    'month':month,
                    'time_zone':'UTC+00:0',
                    'frequency':'1-hourly',
                    'grid':'1.0/1.0',
                    'area':{'lat':[-90,90],'lon':[-180,180]}},
                'workflow_name':'application'}

            # Carry out daily statistics for the specific iteration
            result = c.service('tool.toolbox.orchestrator.workflow',params)

            # Set iteration filename 
            filename = 'ERA5_'+statistic+'_'+variable+'_'+year+month+'.nc'

            # Write filename into filenames.txt file
            w = open(path+'filenames.txt','a')
            w.write(path+filename+'\n')
          
            # Get data URL from result and allow chunking for reading in data
            url = result[0]['location']    
            readurl = requests.get(url,stream=True)
            
            # Write data from URL to filename in chunks
            print('Writing data to: '+path+filename)
            with open(path+filename,'wb') as fh:
                for chunk in readurl.iter_content(chunk_size=1024*1024):
                    fh.write(chunk)
            fh.close()
w.close()