As other answers have said, given enough resources (Methane), your proposed heat engine could work, however I wonder if there could be a more elegant design - especially considering that humans have mastered travel through the solar system.
Since, in your world, humans are now expanding to other planets and moons I think it likely that through the development process engineers would be working on ways to either encapsulate energy for when it is scarce or ways to transmit energy long distances. Since humans are traveling around the solar system in months and spread throughout it there would likely be some sort of infrastructure in place for cargo transport, etc.
If there is no reason that the colony has to be 100% self-sufficient (the energy has to come from Titan), you could take advantage of these cargo routes to transport either fuel or large batteries to colonies with scarce energy along with regular resupply missions. This could be one solution, but the next one I like better:
Wireless Solar Energy Transmission So, you're on Titan. It's cold, dark, full of methane, and you need energy... bad. Luckily the engineers have been working on solutions to maintain a flow of energy to all the colonies.
In a close orbit to the sun, you have an array of large solar collection devices. 199
The concentrated energy is used to generate a laser of a specific wavelength that transmits energy to satellite devices spaced along routes through the solar system. Mirrors/Optic systems could create a constantly unobstructed pathway to all of the satellites as they move through their orbit (or in stationary orbit around another planet). After passing through a relay of these satellite devices, the laser ends its journey at a receiver on the destination planet/moon.
Disadvantages of a laser system such as energy loss through atmosphere wouldn't be an issue transmitting to Titan, but you would certainly not get all of the energy back. This would require a receiver on Titan many hundreds of meters across, and a substantial battery to store the energy as it comes in. Ideally, an unmanned mission would prepare the required infrastructure so that the colonists arrive with several months worth of energy already having been transmitted and stored in the battery.
Similar energy transfer can be done with Microwaves, and to my knowledge the energy conservation is much more effective with Microwaves since you aren't losing so much energy to visible light. Current systems can achieve up to 85% efficiency. Microwave however runs the risk of RF interference (which could be a problem unless the system is positioned away from communication channels) and the receiver would have to be larger than that of a laser.
Here are some stats on current wireless space-solar power systems for reference: 801