Related to "How thermals are found" this question about "Gliding your plane to save fuel" details how to use thermals to save fuel. To use thermals to maximize range, can thermals be mapped in real-time using Doppler or sensors or a data base of some type to fly by?
No. Thermal activity in an area can be predicted in a general way based on atmospheric conditions, but not beyond that. The only way to detect thermals in real time is to stumble into them, and/or locate them by the clouds that form their tops.
In any case, the only conditions for which that sort of thing would work would be on one of those lovely soaring days where steady thermal sources and a moderate wind create "cloud streets" where the cumulus clouds line up for you in rows (the cloud being moisture in the air of thermal condensing at the dew point, creating a handy marker for glider pilots - if the air is dry, the thermals are still there but you have no clouds and you can only find them by trolling).
So it could theoretically work -
If: you had that one day of many where the conditions cooperate and you get decent cloud streets, and
If: the thermals were broad in diameter and,
If: your track just happened to match the direction of the cloud streets, and
If: you cruised just below the cloud bases to make it easy to locate them, and
If: you didn't mind the bumps and surges up and down and didn't have passengers that were prone to airsickness.
In those conditions you could push over and reduce power to maintain speed in the thermals when you feel the upward surge entering it, and then do the opposite when out of the thermal when out of it. You do this automatically anyway when flying on bumpy days, to hold an altitude, although normally it's random as you stumble in and out of lift.
One problem is, between the clouds on the street, the air is sinking, so the period you are in sink cancels out the period you were in lift, to some degree, limiting the benefit pr maybe negating it.
Another problem is you need to slow the airplane down to do this effectively.
Another problem is you have to get good at identifying when you are in lift and in sink and if you have no soaring experience this can be tough.
Now, I do like to take my own homebuilt PL-2 power plane and soar it on good lift days from time to time, by turning it in a "virtual sailplane" by setting power to give a 200 fpm or so sink rate and fly around just above the stall working the lift (the engine is running at about 35-30% power to do this). I call it "power soaring". But I don't do that when going somewhere although I could try to do it cross country if I wanted and was willing to take an hour to go 40 miles.
If you are really serious about saving fuel, forget about trying to exploit thermal lift except as something to do for fun, and where the right opportunity might happen once in a blue moon, and focus on not being in a hurry to get from A to B.
If you aren't in a hurry, you can cruise your airplane at best range speed and power for the maximum MPG (maybe 40-50%), and you can go places in the early morning when the winds are light and the air is smooth, with your engine barely working, and enjoy the scenery sliding by a little bit slower than normal. Best time to be in the air.
If you're renting however, and paying on a Hobbes meter, the benefit of the fuel saving is going to the airplane's owner, not in your pocket.