Hi, i'm a novice when it comes to computers, just recently finished my first build, i'll post the specs for background as it might help in answering my questions. Sorry if it's a bit long, thanks for your time in advance. 
 
CPU: i5-4590
GPU: GTX 970 SSC ACX 2.0+
RAM: 8GB
Case: Cooler Master Elite 130
 
I have several matters i'd like to address.
 
- Whenever i try to play a game for the first time, my TV monitor goes dark and says "no support", when i push the windows key on the keyboard, it takes me to the desktop and i can hear the game running in the background. All of this is always fixed when i go to Geforce Experience and optimize the settings. I've asked someone i know about this and they suggested it might have to do with using a TV and not a monitor, any other ideas/suggestions as to why this is happening? I hope i don't run across a game that Geforce Experience doesn't recognize...
 
- What sort of things should i look after when trying to optimize my GPU? When in the desktop (i.e. using some light programs,) MSI afterburner typically reads GPU1 temperature to be anywhere from 36-45 degrees Celsius. I was told by someone i know that generally, these numbers are good considering the fans don't really spin in these types of conditions (they twitch i've noticed) and that temperatures will likely not go above 80 when gaming.
 
I've played 3 games so far and i don't believe the GPU has gone above 70 degrees. 
 
Can i get some "definitive" information on temperature knowledge/management? Does this sound normal considering the context (case, etc)?
 
- Bonus Question: This question refers to my CPU, i'd really appreciate it if i could get some quick help here too. Originally, i made a mistake and had to reapply thermal compound on the basic intel CPU fan, this resolved an issue i was having where the CPU was reaching the 90's (in degrees Celsius) when playing a game like CS:GO (i was told by someone i know more or less that i shouldn't worried that i may have compromised the CPU as it would typically shutdown before any real damage occurred). Now the CPU when on the desktop runs anywhere from 38-46 degrees on average, with 1 second spikes when something is opened, and when i've played games like CS:GO, Left 4 Dead 2, Team Fortress 2, it's reached top temperatures of 60ish, 50ish, and 55ish respectively.
 
My question is, if i get a new cpu fan how much would the temperatures improve? (one that actually fits in this small case) What can you recommend?
 
I want this to run as quick and "cold" as possible.
 
Thanks for reading, and i appreciate the help. 

Welcome, Bakala.
 
I'll chime in on what I can but with respect to your display, check with the manual to see if there is a specific PC input available.  Monitors are designed to receive inputs from a PC while TV's are not but some work better than others.  
 
The temperatures listed in your first post for the GPU and CPU are both perfectly fine.  GPU can take temps up to 97C (don't want it running that hot though) but under 80C is preferred.  
 
Hopefully someone else can respond to your question on the fan for your CPU cooler.