Kindly check the temperature first with a thermometer. The brain does a lot of work so there is a lot of blood flow to the head which can make it a little warm to touch. However that does not mean fever or sickness. As long as the temp in your thermometer reads normal, there is really no need to worry

Kindly use a thermometer first to know whether the "hotness" is truly something to worry about or not. If the temperature is normal, that is between 36.5 - 37.4, there is no need to worry at all

Mentholatum is just methol and some pain relievers. There's no harm if you want to use but EXTERNAL use only. Don't give to drink or inside the orifices

The case of excessive sweat (hyperhidrosis) is not so common but it does exist. So I'll say relax, dress your child light, singlets and sleeveless bodysuit should be the wears for this weather. Keep your child hydrated, give alot of fluid preferably water..

Is your child not over dressed?
Is the room temperature cool enough?
Is child sweating in an environment where others are not?
If yes to the above questions you will have to take your child to see a paediatric endocrinologist for evaluation and management.