You can check the tps fairly easily using the dealer mode, putting the bike into dealer mode is explained here;
The specifics of checking the tps are outlined in the the FI diagnosis section of the service manual in the downloads area of the site;
https://www.v-strom.co.uk/downloads.htmIf the tps is correct then I would check your fast idle. The manual lists 1800-2400rpm at 25C. With the temperatures we have at the moment, I would expect the bike to run at 2k plus on first fire and take a good few minutes to settle down to normal idle, ideally once the temperature guage has at least 1 if not 2 bars showing.
If both tps and fast idle seem OK then I'd move on to throttle body balance and checking the secondary throttle bodies as well.
* The fact that all seems fine once fully up to temperature would lean me towards the fast idle setting being too low but the tps is an easy check so worth doing anyway. Your symptoms are very similar to how mine behaved and it was fast idle for me.
