When you bore a stock cylinder you will not experience any heating issues.
Most overheating problems are caused in your case by the wrong fuel/oil ratio, by an air leak leaning out the mix, or by incorrect jetting.
Before you pull the motor down it would be a good idea to leak test it, to confirm if it was you who killed it by messing up, or wether it was killed by an air leak.
When you do rebuild you will need a leak tester as you assemble the new top end.
Member Slickerthanyou sells the leaktesters. $33 shipped in the lower 48 states $43 international.
Doing this test is the only way to know that your motor is leak free.
You can also build your own tester, threaded tee, some nipples, tubing, gauge, PVC reducer bushing (for the intake), teflon tape, and a tire valve(schrader), cable ties.