Assuming your wife is expecting to travel on the Bakerloo Line (i.e. the brown one), then at that time of day, it's not likely the trains will be packed rush hour style, since the festivities start earlier and finish later, and are centred a significant distance to the west, and on the Central Line and Hammersmith & City Line. There are likely to be more people changing tube lines than you would get on an average Monday lunchtime, particularly since changing from one Underground line to the other at Paddington can involve walking through the main station. If she's been to London before it will feel much more like a Saturday than a weekday.
The cheaper option is to use the tube for the whole journey, changing from the Piccadilly Line to the Bakerloo at Piccadilly Circus, but that is likely to feel significantly more crowded/oppressive than catching the Heathrow Express, will take significantly longer, and Piccadilly Circus is never a particularly quiet station, particularly over a national holiday.
The most expensive options are to take a taxi, either from Heathrow or from Paddington. If using a cab all from Heathrow, there are road closures due to the carnival, but I don't think they'll affect some of the more obvious routes, and her cabbie should be aware of them. Both these options would also avoid most of the difficulties with steps and luggage that using the tube will have. Having said that, it's not a particularly pleasant or beautiful trip from either point, involving either a motorway, or the second most polluted road in London.