Some points:
1) The MAXIMUM cutoff for the i7-3770K is 105degC I believe.
2) It's almost impossible to damage a modern CPU. When it reaches a certain temperature it DOWNCLOCKS to protect itself and if it gets to the danger zone it will just crash your PC to protect itself.
3) 80degC under max load at 3.8GHz seems normal with that cooler, depending on the ambient temperature. *HOWEVER, that cooler's fan will still be much noisier than a better cooler with a better fan (like Noctua).
4) Yes, you can take the CPU apart (there are videos) and use good thermal paste to improve cooling but I don't recommend that for most.
5) If your CPU doesn't crash under maximum load it will be perfectly fine and much cooler under any other load.
6) It's possible to get the i7-3770K to about 4.1GHz while still maintaining its power management features (in idle it will drop frequency and voltage to use less power and reduce fan noise).
7) Even with an HD7970 or GTX680 overclocking beyond 3.9GHz for most games will provide little benefit.
8) Some CPU temperature monitoring programs:
a) are incorrect, or
b) use motherboard, not CPU sensors.
Your temperatures appear correct so it's likely the monitoring program works properly.
9) One indicator that the thermal paste/cement that's inside your CPU is spread incorrectly is more than a 5degC difference between cores when all 4C/8T are under max load.
10) Fans/coolers. On a side note, many people don't have enough fans or don't have proper fan control to reduce noise.
a) fans are either VOLTAGE (3-pin) or PWM (4-pin) and for proper fan control you need the proper fan for your motherboard AND for the BIOS and motherboard to be properly setup (I recommend setting a manual ramp of LOWEST fan speed until about 40degC and then a slower ramp to 60degC then a sharper ramp from 60 to 80degC. It depends on the software what you can apply.)
b) In a gaming system you should always have at least one front fan, and at least one top/rear fan in-line with the CPU fan to exhaust the heat. If possible use the proper Voltage/PWM fans so you can also control their fan speed via the motherboard and motherboard software.
c) The Corsair H100i is a great CPU cooler, however you require a compatible case, it's over $100 and you still need to setup the fans to ensure optimal noise control.
d) Noctua makes awesome fans. It's surprising how significant the difference in noise can be. I replaced my FOUR case fans with TWO Noctua (12cm PWM) and also had to replace my Noctua NH-D14 fan with one PWM Noctua fan. So my CPU fan, front case, and top/rear case each have a 12cm Noctua PWM fan that's speed-controlled. My graphics card is an Asus GTX680 TOP (3-slot) so it runs cool and quiet.
Summary:
- your results are normal
- replace the CPU cooler only if it's too noisy under normal gaming load
- verify proper air movement in case (many people forget the front case fan)
- CPU can have thermal paste redone (videos on line) but do so ONLY if necessary. I don't recommend for most.