Have you a fan you can face towards your baby, but not too close, as a room temperature of 24C is too hot, but we can't do much about room temperatures in the UK as air conditioning is not usual in domestic homes here.
Older healthy children, and most adult bodies, are able to regulate our internal temperatures between quite a large difference in outside temperatures (as long as we "listen" to our bodies and drink - and to some extent eat - when our bodies are telling us too. They (our bodies) can also tell us to take off or put more clothing on, seek shade or sources of heat etc. But young children, the elderly and the infirm, have either not yet acquired that ability, or have lost it again - I'm in the losing it again camp these days!
If you can't do anything about the room temperature, and if your baby's temperature keeps fluctuating (and stops responding to the Calpol), then I think that you should ring 111 for advice - I would expect them to respond to a baby's temperature of even 39C% temperature within 20 minutes to half an hour maximum.
By the way, stripping a small child's clothes off (you can keep the nappy on) and sponging them with tepid water - where if you put it on the inside of your arm and the water doesn't seem cold or warm to you, or only a little bit warm - can help them cool down more quickly, but don't dry them. The slightly warm water actually evaporates more quickly than cold water, and therefore cools the child down more quickly. You should only need to sponge the areas that the baby is not lying on, and don't do their hands or feet - the extremities could potentially get a bit too cold, but that may just be me being over cautious with babies...
If your dear little one's temperature doesn't settle, but keeps on going back up to 40+% more often than you can keep giving Calpol, then I do think that a visit to your nearest A&E is advisable.
Some 💐 for you @BeALovingFamily because I know how worrying it is when our children aren't well, and also the probable reduction in sleep for the caregiver can just make it all that much harder. Is there anyone who could help you with your other children in the morning?