Surprised it was giving any values at all!
I think you want no colon on the name, and the degrees symbol in the unit:
template:
sensor:
- name: Heizung Esszimmer Temperatursensor
state: "{{ state_attr('climate.smart_thermostat_210940168395749','current_temperature')}}"
unit_of_measurement: "°C"
device_class: temperature
state_class: measurement
…and note that you’ll only get the graph once the old unit-less measurements have “expired” from the graph window.