Does it make sense to turn a closed Mac upside down when it's hot?
There is no need to do anything special with regards to your Mac feeling hot. Your Mac's fans are managed by the System Management Controller (SMC) which will ensure that your CPU etc are protected in the event your Mac overheats to the point that it could cause damage.

Your question doesn't actually specify what temperature your Mac is at, so it's impossible to comment on whether it's too high. However, MBP models usually range from about 40ºC (104ºF) to 100ºC (212ºF) depending on whether the CPU is idle or under load. CPU temps (just like ambient temperatures) typically have a bearing on GPU temps too, especially within the extremely confined spaces of a MacBook. 

If you'd like, you can refer to the Intel Mac Temperature Database to see the various temperature ranges reported by users. You can also filter the list by model etc.

If you're still concerned, you can also Reset the System Management Controller (SMC) on your Mac to see if this has any noticeable impact on what you're experiencing.