If you run out of tape, tell the manufacturer you ran out and need more. It will likely be sent for free. The long rolls of double sided tape that is fairly weak so as not to lift paint are not widely available to buy on their own.
Stick a small piece of tape onto the frame. If the tape pulls off very easily, there is moisture or grease on the frame. Clean off grease with a rag and residue-free solvent such as methylated spirits or white spirit (apparently common in the UK) or rubbing alcohol (common in the US). Wipe off moisture and use gentle heat to evaporate away any that remains. Turn up the thermostat several degrees, or operate a space heater in the general area of the window. Make sure any humidifier has been turned off and you haven’t boiled or washed anything with hot water for a few hours. Metal frames are more difficult. It is harder to remove the moisture from metal framed windows because the cold metal attracts fresh moisture very quickly. Metal frames must be smooth; any loose paint or rust should be removed. Just use a plastic brush to scrub off the excess; leave marring them more or exposing more of a vulnerable surface for repainting time.
If the tape comes off the sill later, you can fix the problem with clear mailing tape (which doesn’t look quite perfect and can lift paint).
Be very careful to stand so that you would not fall onto the window if you fall, and to extend the knife very little and hold it so that you would be unlikely to cut yourself badly in case of an accident.
If the hair dryer turns off on its own, it has probably overheated. It probably has a thermal protector that will reset itself if the dryer is unplugged and allowed to cool for up to a half-hour.
