It's not just heart rate it's power as well.
45 minutes at a moderate endurance power (about 60-65% of FTP) on the road is a doddle but doing it on the Turbo is a real killer. Perceived effort would go from about 5 to 9.
I think some of us are simply not suited to turbo trainers
I would suggest you stick at it and build up to 20 minutes over a couple of weeks.
Bear in mind as well that you should be seeing your heartrate increase over the course of the session so don't worry about starting off below your target rate (or finishing above it).