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Hi,
I think there is an issue with memory allocating with threading.Timer in 3.8.0/3.8.1.
When I run the attached code in Python 3.7.3 I get a memory consumption of approx. 10 MB. If I run the same code with python 3.8.0 or 3.8.1, it keeps consuming memory (several hundreds of MB). 
I've attached 3 images where I run the attached script under mprof.
By inspect of the output from tracemalloc, I can see that 
/usr/lib/python3.8/threading.py:908 keeps allocating memory.
I have tested this with python 3.8.0 from ubuntu 16.04 repository and python 3.8.1 from source. Both versions suffers from the memory consumption issue.

This issue also affects me, pyth. I tried it out with various combinations of sleep, and durations of tasks, but what I noticed is that threading_shutdown_locks continues to grow at each iteration.
for i in range(100000):
 for j in range(10):
 timer = threading.Thread(target = callback)
 timer.start()
 time.sleep(1)
 print(len(threading._shutdown_locks))
If I accumulate the Timer/Thread s and join them, then the _shutdown_locks will be cleared.

Please include the script as an attachment or text so that it will be easy to view them. The script as below from the attachment : 
import threading
import time
import tracemalloc
def callback():
 pass
tracemalloc.start()
for i in range(100000):
 snapshot1 = tracemalloc.take_snapshot()
 for i in range(100000):
 timer = threading.Timer(1, callback)
 timer.start()
 snapshot2 = tracemalloc.take_snapshot()
 top_stats = snapshot2.compare_to(snapshot1, 'lineno')
 print("[ Top 10 differences ]")
	
 for stat in top_stats[:10]:
 print(stat)

I filed a bug for this a few weeks ago, and then found another ticket about the same issue before:
https://bugs.python.org/issue37788
My ticket: 
https://bugs.python.org/issue39074
The memory leak was from a change introduced about 6 months ago:
https://github.com/python/cpython/commit/468e5fec8a2f534f1685d59da3ca4fad425c38dd 

I close this issue as a duplicate of bpo-37788.