No need to convert it as HA internally treats its states as strings anyway. You just have to define the type key in your knx expose for the knx Integration to encode it properly when sending to the bus (because it can’t know the DPT). See Value types and Expose
But I see you used “temperature” so it should work. Be aware that the knx Integration only sends on state changes (and init).
Try enabling debug log for xknx.telegram and look for the GA when a state changed. Log level
Here you can find the proper entity_id
And here if any errors occur in the logs