Regarding the hardware behind it, this is voluntarily not documented by Microsoft as answered elsewhere by an employee :
"We will not provide performance metrics on temp drive has it varies with every VM size. Hence it's not been documented and since temp drive are provided to VMs, from underlying compute machine itself the read/write operations will be fast. However it can't be expanded or increased based on requirement. You may have to increase the size of VMs if you need more temp drive space and if that temporary files are important, then you need to go for premium disks as it provide persistent data."
I would be against storing logs on it as you could loose them and they can matter a lot depending of the situation.
It seems that putting TempDB on the temp drive is recommended : https://learn.microsoft.com/en-us/azure/azure-sql/virtual-machines/windows/performance-guidelines-best-practices
"Place TempDB on the local SSD D:\ drive for mission critical SQL Server workloads (after choosing correct VM size)." (D: being the temp drive)