Universe is not theoretically infinite; The energy content within is not infinite; the 'volume' of space is not infinite. They are simply mind-bogglingly vast.
I believe the Big Bang theory, as it is the only theory we currently have that explains all the available data. From this it follows, that the universe is expanding and current models seem to indicate that the universe will not experience a Big Crunch. This leads to the universe expanding until the end of time (if such point will ever even come). So, theoretically, the universe will be expanding until infinity come, but since it can never come, the volume of the universe will increase forever but at any single point in time it will, theoretically, be still measureable.
This means that the end will not be the end of the universe, but rather the end of baryonic matter or energy available for work (in the physics sense of the word). How will this come about? The timeline mainly depends on if protons are in fact unstable or not. If they are unstable, they will begin to experience decay (as happens contantly in radioactive materials) and fall apart after a sufficient amount of time (that is, 10 to the power of 31 to 41 years, or 1 followed by 31 to 41 zeroes in years. For reference, the current age of the universe is about 14 billion years, or 14 followed by nine zeroes). In the end, what will be left is a cold expanding universe where space of several cubic parsecs in size will contain less than a single photon's worth of energy. There will be no light, no heat, no stars, no matter itself (as we know it). The energy available for work in the universe will be brought down to nothing as the second law of thermodynamics degrees.
On the other hand, if the protons are not unstable, the 'end' will come about by the way of black holes formed from stellar mass objects and quantum tunnelling leading to all matter slowly transforming into iron. This takes tens of orders of magnituted longer than the protonic decay scenario. But in the end, the result is the pretty much same. No heat, no energy. A cold dead universe, still expanding in size.
That is the almost inevitable end for everything, irregardless of our technology in the billions of years to come. The only escape from this, is the theory of alternative universes and even then, we would need to find a way to breach the barriers between that universe and us, and even that universe would be on it's way to dying like ours is. Nothing lasts forever.