X-Prizes (which is both a somewhat generic term and a trademark to one company), which are basically one-off large-ish payments ($1M and up) to the winner of a particular contest or the first company to achieve a particular goal. They don't necessarily grow the manufacturing stage but they can kickstart the early prototyping/tinkering stage, provided this is an interesting problem which has not seen enough early research.
$1-10M is a drop in the bucket for any kind of government-led industrial initiative and the nice thing is that they can be extremely targeted to a particular subject of interest.
Not the first, but perhaps the first to really impact a contemporary industry (autonomous driving) and catch the public attention was the 2004 DARPA challenge
No team entry successfully completed the designated DARPA Grand Challenge route from Barstow, CA, to Primm, NV, on March 13, 2004. The event offered a $1 million prize to the winner from among 15 finalists that emerged from a qualifying round at the California Speedway, but the prize went unclaimed as no vehicles were able to complete the difficult desert route.
A year later, on October 8, 2005, another round of the Grand Challenge was held in the desert Southwest near the California/Nevada state line. The Stanford Racing Team won the $2 million prize with the winning time of 6 hours, 53 minutes. A total of five teams completed the Grand Challenge course which was 132 miles over desert terrain.
Yes, the above is DARPA's own verbiage, but it does reflect the excitement many felt at the improvements between the 2004 and 2005 runs.
In the beginning of aviation there were, IIRC, a number of prizes available to doing things like crossing the Channel (Daily Mail £1000, 1911) and they were also instrumental in growing the field quickly.
I don't have one for heat pumps, but there is a climate related one for CO2 scrubbing and sequestration: $100M, run by Elon Musk.