Three hours is plenty of time, the legendary long lines of Heathrow are mostly history.

If your luggage is checked through, then the easiest thing to do is to take the airside bus to T3. Once there, you'll need to get your onwards boarding pass and re-clear security. (The bus saves you the need to go through UK passport control.) This probably puts you in T3 60-90 minutes after arriving.

If you need to collect your luggage and re-check it, then you'll need to clear UK passport control, pick up your luggage, and walk (it's about a 15 minute walk) over to T3. You can get there by taking the tunnel towards the Heathrow Express station. The time here is much more variable, as it depends on lines at arrivals, the wait for your luggage, wait to checkin, etc. If you have status on the departing airline this should take a similar amount of time.