MongoDb get last and max values with timestamps - mongodb

Question

I am new to MongoDb as I only installed it yesterday...
I have a collection of temperature readings from n rooms:
[
{
"key": "livingRoom",
"name": "Living Room",
"temp": 19.437,
"ts": "2017-04-29T07:20:22.000Z"
},
{
"key": "bedroom",
"name": "Bedroom",
"temp": 24.875,
"ts": "2017-04-29T07:21:14.000Z"
}
]
and I want to get the current (last) temperature and the min/max over the last 24 hours for each room. I also want the timestamp of the min and max values.
I am 90% of the way there but as always that last 10% seems to take 90% of the time.
I have this aggregation:
{
"$group": {
"_id": "$key",
"temp": {"$last": "$temp"},
"name": {"$last": "$name"},
"ts": {"$last": "$ts"},
"maxTemp": {"$max": "$temp"},
"minTemp": {"$min": "$temp"}
}
}
That produces this result:
[
{
"_id": "bedroom",
"temp": 22.25,
"name": "Bedroom",
"ts": "2017-04-30T07:31:30.000Z",
"maxTemp": 24.875,
"minTemp": 21.437
},
{
"_id": "livingRoom",
"temp": 18.75,
"name": "Living Room",
"ts": "2017-04-30T07:39:38.000Z",
"maxTemp": 19.625,
"minTemp": 17.625
}
]
but of course that doesn't include the timestamp of the min and max values.
This question:
Multiple group operations using Mongo aggregation framework was useful and seems to indicate that I can't do what I want to.
I was planning on using different groups with different sorts to get the different aggregations that I want but as a group acts on the result of the last group it seems that what I am trying to do can't be done by mongo.