Tony, I have improved upon your suggestion for an invention. However, I regret to report that I don't have a shed to work in; instead, I have resorted to a makeshift workspace in our downstairs loo.
The proposed combination of heat-sensitive pad, mug, tea bag, timer, and alarm presents too many parts that could potentially fail, spoiling the process. Fortunately, with perseverance, I have overcome the lack of an appropriate workspace, and invented a device that simplifies the process, and eliminates some functioning parts, and steps as well, resulting in a more restful process with less labor.
My device is simple, and constructed of a broad inverted cone (point down), to which a second narrow steep-sided inverted cone has been fused at the point of the broad cone. A hole connects the two cones. The broad cone is the in-fluent cone, the narrow cone has an effluent orifice at it's base.
Operation is simple. You could do this in other locations, but I found the sink in the loo to be well-suited for testing purposes. Place the dual-cone device point-downward in the sink. A teabag is first placed in the in-fluent cone, and a measured volume of hot water is then poured into the in-fluent as well. The process could take awhile, I recommend laying down for a nap until the process is finished. You will note several advantages. First, there is no mug to wash up, the cone device easily rinses clean. Second, the only waste produced is the teabag, the contents of the teabag may be composted. Third, the timer and alarm have been eliminated, allowing the nap to proceed naturally and uninterrupted by jarring alarm noises. After your tea time, you will wake naturally, and feeling refreshed.
No need to thank me. I can send you as many of the dual-cone devices as you want for a mere £250 each, plus shipping and handling.