Question

CREATE TABLE #TEMPTABLE
(
     requestTime datetime2,
     NoOfSessions integer

)

INSERT INTO #TEMPTABLE
select  convert(nvarchar(16), TimeLog, 120) requestTime , COUNT(DISTINCT SessionId)As NoOfSessions
from  LogData
group by convert(nvarchar(16), TimeLog, 120) order by requestTime;


select  s1.requestTime
,       (
        select  sum(NoOfSessions)
        from    #TEMPTABLE s2
        where   dateadd(minute, -15, s1.requestTime) < s2.requestTime
                and s2.requestTime <= s1.requestTime
        ) as TotalNumberOfSessions
from    #TEMPTABLE s1


DROP TABLE #TEMPTABLE

Answer 1

Try this and let me know. It might be some improvement for you.
I added a primary key on requestTime in the temp table that can be used in the correlated sub query.

create table #TEMPTABLE
(
  requestTime smalldatetime primary key,
  NoOfSessions integer
)

insert into #TEMPTABLE
select dateadd(minute, datediff(minute, 0, TimeLog), 0), 
       count(distinct SessionId)
from  LogData
group by dateadd(minute, datediff(minute, 0, TimeLog), 0)


select  s1.requestTime
,       (
        select  sum(NoOfSessions)
        from    #TEMPTABLE s2
        where   dateadd(minute, -15, s1.requestTime) < s2.requestTime
                and s2.requestTime <= s1.requestTime
        ) as TotalNumberOfSessions
from    #TEMPTABLE s1

drop table #TEMPTABLE