is Nest App or Google home capable of tracking thermostat set vs actual temperature?

[dukebdevil]

I had a new HVAC system installed last year and the AC is not performing (ie: cannot maintain set temperature during the day).  I know why (lack of CFM from the "intelligent" system) but I am looking for the data points to show that the actual indoor temperature is rising even with the system running.  would be nice to plot 
time    set    actual

0900  74      72

1100    74       75

1300    74      77   

2100    74      80   (outdoor 78)

Thanks.
PS  is there a REST API for the Nest?  a python module?

[dukebdevil]

apparently, there is a REST API for the Nest
'https://developer-api.nest.com/devices/thermostats/YOUR_THERMOSTAT_ID'
next need documentation and access